Other uses File Soliton hydro.jpg thumb 250px Solitary wave water waves Solitary wave in a laboratory wave channel. In mathematics and physics , a soliton is a self reinforcing solitary wave a wave packet ... partial differential equation s describing physical systems. The soliton phenomenon was first ... . Definition A single, consensus definition of a soliton is difficult to find. harvtxt Drazin .... Moreover, some scientists use the term soliton for phenomena that do not quite have these three ... soliton for water waves. The blue line is the carrier wave s, while the red line is the Envelope mathematics envelope soliton. Dispersion and non linearity can interact to produce permanent and localized ... a soliton. See soliton optics for a more detailed description. Many exactly solvable model s have soliton ... nonlinear Schr dinger equation, and the sine Gordon equation . The soliton solutions are typically ... vast linear roll cloud s. The recent and not widely accepted soliton model in neuroscience proposes to explain the signal conduction within neuron s as pressure solitons. A topological soliton , also ... against decay to the trivial solution. Soliton stability is due to topological constraints, rather ... has been repeated in many papers and books on soliton theory. ref I was observing the motion of a boat ... in the history of the development of soliton theory. ref In 1965 Norman Zabusky of Bell Labs and Martin Kruskal of Princeton University first demonstrated soliton behaviour in media subject to the Korteweg ... equation has since extended this to solution of many related soliton generating systems. Solitons in fiber optics See also Soliton optics Much experimentation has been done using solitons in fiber ... . ref cite web url http tappert.us fred reminiscences on optical soliton research.pdf title Reminiscences on Optical Soliton Research with Akira Hasegawa author Fred Tappert date January 29, 1998 .... He also proposed the idea of a soliton based transmission system to increase performance of optical ... more details
wiktionary soliton A soliton is a type of self reinforcing solitary wave. Soliton may also refer to Soliton optics , an optical field that does not change during propagation because of a balance between nonlinear and linear effects Soliton topology , a solution of a system of partial differential equations or of a quantum field theory homotopically distinct from the vacuum solution Soliton Incorporated , company Soliton model , neurological model disambiguation ... more details
Soliton Incorporated was a company formed in 1993 to continue the support and development of Sharp APL, originally developed by I. P. Sharp Associates , and other related products and services. History Soliton Incorporated was formed in 1993 in Toronto, Ontario, Canada with some of the former employees of I. P. Sharp Associates . The business was in some ways a continuation of I. P. Sharp Associates , which was purchased by Reuters in 1987. Reuters was primarily interested in Sharp s historical databases, and allowed some portions of the business to buy themselves out from Reuters. The company started with Clarke Bruce as its president. Timeline 1987 I. P. Sharp Associates is bought by Reuters 1993 Soliton Incorporated is founded 1997 Soliton develops TimeSquare, a timeseries database with an SQL like syntax See also I. P. Sharp Associates ict company stub External links http www.thocp.net software languages apl.htm APL programming language Chronology Category Technology companies of Canada ... more details
Context date October 2009 In physical optics or wave optics , a vector soliton is a solitary wave with multiple ... have two distinct polarization components. Among all the types of soliton s, optical vector solitons ... exchange between the two polarizations of the vector soliton which may induce intensity differences ... components of the vector soliton. Researchers have obtained both analytical and numerical ... and Joseph first theoretically predicted a novel form of phase locked vector soliton in birefringent dispersive media, which is now known as a high order phase locked vector soliton in SMFs. It has ... locked vector soliton but also a polarization locked vector soliton. They reported that the intensity .... Soc. Am, B 17, 354 2000 . ref However, recently, another type of vector soliton, induced vector soliton has been observed. Such a vector soliton is novel in that the intensity difference between the two ... unable to form a component of a vector soliton. However, due to the cross polarizaiton modulation between strong and weak polarization components, a weak soliton could also be formed. It thus demonstrates that the soliton obtained is not a scalar soliton with a linear polarization mode, but rather a vector soliton with a large ellipticity. This expands the scope of the vector soliton so that the intensity ratio between the strong and weak components of the vector soliton is not limited to 0.25 ... concerns a high order phase locked vector soliton in SMFs, a stable high order phase locked vector soliton has recently been created in a fiber laser. It has the characteristic that not only are the two orthogonally polarized soliton components phase locked, but also one of the components has a double ... the soliton dynamics but instead two coupled NLSEs are required. Then, solitons with two polarization ... are generated? FWM spectral sideband in vector soliton A new pattern of spectral sidebands was first experimentally observed on the polarization resolved soliton spectra of the polarization locked ... more details
A soliton distribution is a type of discrete probability distribution that arises in the theory of erasure correcting code s. A paper by Luby ref name Luby Luby, M. 2002 , http ieeexplore.ieee.org xpl freeabs all.jsp?arnumber 1181950 LT Codes , The 43rd Annual IEEE Symposium on Foundations of Computer Science ref introduced two forms of such distributions, the ideal soliton distribution and the robust soliton distribution . Ideal distribution The ideal soliton distribution is a probability distribution on the integers from 1 to N , where N is the single parameter of the distribution. The probability mass function is given by ref name T Tuomas Tirronen 2005 http citeseerx.ist.psu.edu viewdoc download?doi 10.1.1.140.8104&rep rep1&type pdf Optimal Degree Distributions for LT Codes in Small Cases , Helsinki University of Technology. ref math p 1 frac 1 N , math math p k frac 1 k k 1 qquad k 2,3, dots,N . , math Robust distribution The robust form of distribution is defined by adding an extra set of values to the elements of mass function of the ideal soliton distribution and then standardising so that the values add up to 1. The extra set of values, t , are defined in terms of an additional real values parameter &delta which is interpreted as a failure probability and an integer parameter M M < N . Define R as R N M . Then the values added to p i , before the final standardisation, are ref name T math t i frac 1 iM , qquad qquad i 1,2, dots,M 1 , , math math t i frac ln R delta M , qquad i M , , math math t i 0, qquad qquad i M 1, dots,N . , math While the ideal soliton distribution has a mode statistics mode or spike at 1, the effect of the extra component in the robust distribution is to add an additional spike at the value M . See also Luby transform code References reflist Category Discrete distributions Category Coding theory ... more details
File Soliton de Peregrine.png thumb upright 1.8 3D view of the spatio temporal evolution of a Peregrine soliton The Peregrine soliton is an analytic solution of the nonlinear Schr dinger equation . ref ... soliton that can maintain its profile unchanged during propagation, the Peregrine soliton presents a double ..., the Peregrine soliton develops undergoing a progressive increase of its amplitude and a narrowing .... These features of the Peregrine soliton are fully consistent with the quantitative criteria usually used in order to qualify a wave as a rogue wave . Therefore, the Peregrine soliton is an attractive ... V.V. year 2009 title What makes the Peregrine soliton so special as a prototype of freak waves ? journal J. Eng. Math. ref Mathematical expression In the spatio temporal domain File Peregrine soliton profile.png thumb upright 1.4 Spatial and temporal profiles of a Peregrine soliton obtained at the point of maximum compression The Peregrine soliton is a solution of the one dimensional nonlinear ... for math xi 0 math and math tau 0 math . The Peregrine soliton is a first order rational soliton. It can ... soliton ref name PLA Akhmediev It is also possible to mathematically express the Peregrine soliton .... Experimental demonstration File Peregrine soliton in optics.png thumb upright Record of the temporal profile of a Peregrine soliton in optics ref name OL Hammani cite journal title Peregrine soliton ... where the Peregrine soliton has been for the first time experimentally generated and characterized ... first7 N. last8 Dudley first8 J.M. year 2010 title The Peregrine soliton in nonlinear fibre optics .....790K ref ref cite web title Peregrine s Soliton observed at last publisher bris.ac.uk url http www.bris.ac.uk ... been exploited in the past in order to generate Soliton optics optical solitons in optical fibers ... , a profile very close to the ideal Peregrine soliton can be generated. ref name OL Hammani ref cite ... Rogue wave Notes and references reflist Commons category Peregrine soliton DEFAULTSORT Peregrine Soliton ... more details
Cleanup date July 2007 In optics , the term soliton is used to refer to any optical field that does not change ... as solitons in optics. Spatial solitons Image Soliton lens equivalent.svg right 250px how a lens works In order to understand how a spatial soliton can exist, we have to make some considerations about ... effect and we will not notice any nonlinear behavior. The optical waveguide the soliton creates while ... soliton math a xi, zeta operatorname sech xi e i zeta 2 math where sech is the Hyperbolic function ... function of z with period math zeta pi 2 math . class wikitable Image Soliton 1st order.svg thumb right 300px Soliton s shape while propagating with N 1, it does not change its shape Image Soliton 2nd order.svg thumb right 300px Soliton s shape while propagating with N 2, it changes its shape periodically For soliton solutions, N must be an integer and it is said to be the order or the soliton ... order soliton at the beginning it has a shape of a sech , then the maximum amplitude increases ... if we want to generate a fundamental soliton is obtained expressing N in terms of all the known ... 85 90047 1 title Propagation soliton et auto confinement de faisceaux laser par non linearit optique ... Temporal soliton explanation.svg thumb 300px right linear and nonlinear effects on Gaussian pulses ... of optical solitons. He also proposed the idea of a soliton based transmission system ... of a dark soliton , in an optical fiber. In 1988, Linn Mollenauer and his team transmitted soliton pulses over 4,000 kilometers using a phenomenon called the Raman effect , named for the Indian ... f x,y math . We make a small approximation, as we did for the spatial soliton math beta 2 omega beta ... 2 eta 0 n k 0 n 2 n frac A m 2 2 eta 0 a 2 math for duality with the spatial soliton, we define math .... The first order soliton is given by math a tau, zeta operatorname sech tau e i zeta 2 math the same ... create such a soliton using slightly wrong power or shape, then it will adjust itself until it reaches ... more details
doi 10.1016 0022 5193 77 90178 3 pmid 886872 issue 2 ref Soliton s in which the energy is distributed ... soliton which Spontaneous symmetry breaking spontaneously breaks the local translational and helical ... group . math n, alpha math ref name Scott1992 cite journal author Scott AS title Davydov s soliton ... Davydov s soliton are similar to some that have been developed in polaron theory. In this context the Davydov s soliton corresponds to a polaron that is i large so the continuum limit approximation is justified ... bandwidth. ref name Scott1992 The Davydov soliton is a quantum quasiparticle and it obeys Heisenberg ... by construction. ref name Scott1992 Supposing that the Davydov soliton is localized to 5 turns of the helix results in significant uncertainty in the velocity of the soliton math Delta v 133 math m s, a fact that is obscured if one models the Davydov soliton as a classical object. There are three ... motions are treated classically. References reflist 2 particles DEFAULTSORT Davydov Soliton Category ... more details
Origin of the soliton concept DSs have been experimentally observed for a long time. Helmholtz ... of localized anode spots in long gas discharge tubes. Nevertheless, the term soliton was originally ... the term soliton was coined by Norman Zabusky Zabusky and Martin David Kruskal Kruskal ref N. J. Zabusky ... . From 1965 up to about 1975, a common agreement was reached to reserve the term soliton to pulse ... the concept of a classical soliton can still be used in the sense that on a short time scale ... losses into account as a perturbation, and on a long scale the amplitude of the soliton will decay ..., vector dissipative soliton could also be observed in a fiber laser passively mode locked through ...,multiwavelength dissipative soliton in an all normal dispersion fiber laser passively mode locked ... single , dual and triple wavelength dissipative soliton can be formed in the laser. Its generation mechanism can be traced back to the nature of dissipative soliton. ref http www.opticsinfobase.org abstract.cfm?URI oe 17 15 12692 H. Zhang et al, Multi wavelength dissipative soliton operation of an erbium ... analytical solutions. See also soliton vector soliton fiber laser Nonlinear system compacton , a soliton ... , a soliton with a non differentiable peak. Q ball a non topological solitonSoliton topological . Soliton optics Soliton model of nerve impulse propagation Spatial soliton Solitary wave s in discrete ...., Advances in Physics 59 2010 485 DEFAULTSORT Dissipative Soliton Category Solitons Category Self organization ... more details
The Soliton model in neuroscience is a recently developed biological neuron models model that attempts to explain how signals are conducted within neuron s. It proposes that the signals travel along the cell s cell membrane membrane in the form of certain kinds of sound or density pulses known as soliton s. As such the model presents a direct challenge to the widely accepted Hodgkin Huxley model which proposes that signals travel as action potential s voltage gated ion channel s in the membrane open and allow ion s to rush into the cell, thereby leading to the opening of other nearby ion channels and thus propagating the signal in an essentially electrical manner. History The Soliton model was developed beginning in 2005 by Thomas Heimburg and Andrew D. Jackson, ref cite journal author Heimburg, T., Jackson, A.D. title On soliton propagation in biomembranes and nerves journal Proc. Natl. Acad ... with the Soliton model. Further, it has been observed that a signal traveling along a neuron ... with the Soliton model. It is undeniable that an electrical signal can be observed when an action potential propagates along a neuron. The Soliton model explains this as follows the traveling soliton ... . Formalism The soliton representing the action potential of nerves is the solution of the partial ... periods in the soliton theory for nerves and the locust femoral nerve year 2010 pmid 21177017 doi 10.1016 ... ref Role of ion channels The Soliton model explains several aspects of the action potential, which ... nor with pharmacology. The soliton model predicts membrane current fluctuations during the action potential ... of the soliton model. Application to anesthesia The authors claim that their model explains ... the soliton model and agrees reasonably well with experimental observations. See also Biological neuron models Hodgkin Huxley model Vector soliton Sources http www.ku.dk english news ?content http www.ku.dk ... Reflist DEFAULTSORT Soliton Model Category Cellular neuroscience Category Computational neuroscience ... more details
In quantum field theory , a non topological soliton NTS is a field configuration possessing, contrary to a topological one, a conserved Noether charge and stable against transformation into usual particles of this field for the following reason. For fixed charge Q , the mass sum of Q free particles exceeds the energy mass of the NTS so that the latter is energetically favorable to exist. The interior region of an NTS is occupied by vacuum different from surrounding one. Thus a surface of the NTS represents a domain wall , which also appears as a topological defect in field theories with broken discrete symmetry ref A.Vilenkin , Phys.Rep.121 1985 263. ref If infinite, the domain walls cause contradiction with cosmology. But the surface of an NTS is a closed finite wall so, if it exists in the Universe, it does not cause those contradictions. Another point is that if the topological domain wall is closed, it shrinks because of wall tension. As for the NTS surface,it does not shrink since the decreasing of the NTS volume would increase its energy. Introduction Quantum field theory has been developed to describe the elementary particles. However in the mid seventies it was found out that this theory predicts one more class of stable compact objects non topological solitons. The NTS represents an unusual coherent state of matter, called also bulk matter. Models were suggested for the NTS ... Image Twof.jpg thumb 250px The non topological soliton configuration for a couple of interacting fields ... onto photons . ref A.E.Everett, Phys.Rev.D 10 1974 3126 ref Soliton stars Q star Image ... hadron field theory. Soliton star If the scalar field potential math U sigma math has two ..., Phys.Rev.D 35 1987 3640 ref and fermion ref T.D.Lee, Y.Pang, Phys.Rev.D 35 1987 3678 ref soliton ... Such objects are called minisoliton stars because of their microscopic size. Non topological soliton .... References references DEFAULTSORT Non Topological Soliton Category Quantum field theory Category Solitons ... more details
In mathematics and physics, a solitary wave can refer to The solitary wave water waves or wave of translation, as observed by John Scott Russell in 1834, the prototype for a soliton. A soliton , a generalization of the wave of translation to general systems of partial differential equations A topological defect , a generalization of the idea of a soliton to any system which is stable against decay due to homotopy theory mathdab zh ... more details
Modified Mexican hat , Modified Morlet and Dark soliton or Darklet wavelets are derived from Hyperbolic function hyperbolic sech bright soliton and hyperbolic tangent tanh dark soliton pulses. These functions are derived intuitively from the solutions of the nonlinear Schr dinger equation in the anomalous and normal dispersion regimes in a similar fashion to the way that the Morlet and the Mexican hat are derived. The modified Morlet is defined as math psi 2 t C psi 2 cos omega 0 t rm sech t math mathanalysis stub Category Wavelets ... more details
Summary Image of a dissipative soliton in planar DC gas discharge by H. U. Boedeker, see also http www.uni muenster.de Physik.AP Purwins DC index en.html Licensing self GFDL cc by sa 2.5,2.0,1.0 migration relicense Copy to Wikimedia Commons bot Fbot priority true ... more details
Summary Image of a dissipative soliton with oscillatory tails in planar DC gas discharge by H. U. Boedeker, see also http www.uni muenster.de Physik.AP Purwins DC index en.html Licensing self GFDL cc by sa 2.5,2.0,1.0 migration relicense Copy to Wikimedia Commons bot Fbot priority true ... more details
Tau function may refer to Tau function Ramanujan tau function , giving the Fourier coefficients of the Ramanujan modular form. Divisor function , an arithmetic function giving the number of divisors of an integer. tau function representation theory Tau function in the representation theory of affine Lie algebra s and integrable system soliton equations . disambig Long comment to prevent listing on Special Shortpages.......................................................................... more details
In optics , a nematicon is a soliton optics spatial optical soliton in a nematic liquid crystal . The name was invented in 2003 by G. Assanto ref cite journal author G. Assanto, M. Peccianti, C. Conti title Nematicons Optical Spatial Solitons in Nematic Liquid Crystals journal Opt. Photon. News volume 14 pages 44&ndash 48 year 2003 doi 10.1364 OPN.14.2.000044 bibcode 2003OptPN..14...44A issue 2 http www.osa opn.org Content ViewFile.aspx?id 2093 ref . Nematicons are generated by the special type of nonlinear optics optical nonlinearity that is present in nematic LCs the optical field induced director reorientation. This nonlinearity arises from the fact that the liquid crystal director i.e. the average molecular orientation tends to align along the optical electric field. Nematicons are very easy to generate with a few mW of optical power ref cite journal author J. Beeckman, K. Neyts, X. Hutsebaut, C. Cambournac, M. Haelterman title Simulations and Experiments on Self focusing Conditions in Nematic Liquid crystal Planar Cells journal Opt. Express volume 12 pages 1011&ndash 1018 year 2004 doi 10.1364 OPEX.12.001011 pmid 19474916 bibcode 2004OExpr..12.1011B issue 6 http www.opticsinfobase.org abstract.cfm?URI oe 12 6 1011 http escher.elis.ugent.be publ Edocs doc.php?file P104 013.PDF ref because the nonlinearity has the following properties A very large nonlinear coefficient the nonlinearity is typically eight orders of magnitude larger than that of carbon disulfide . This means that much lower optical power is necessary for obtaining the same refractive index variation. The nonlocal response nonlocality means that the nonlinear response is not limited to the exact location of the optical field . Instead the nonlinear response is spread out. A high nonlocality leads to a stable soliton propagation. A higher and lower power than the ideal soliton power will lead to breathing ... and no further reorientation is possible. See also Soliton optics Liquid crystal References references ... more details
Otheruses Infobox Album See Wikipedia WikiProject Albums Name Futureproof Type Album Artist Pitch Black band Pitch Black Commented out because image was deleted Cover futureproof.jpg Released 1999 Recorded Genre Electronica , dubtronica , downtempo Length 104 31 Label Kog Transmissions Producer Last album This album Futureproof br 1999 Next album Electronomicon br 2000 Futureproof is the debut album released in 1999 by New Zealand band, Pitch Black band Pitch Black . Track listing Disc One The Gatherer 6 37 Speech 8 40 They Are Among Us 9 32 Soliton 11 57 The Gatherer Live 9 17 Altered State 7 58 Alternate State 6 47 Disc Two Melt Dub Obscura Mix 6 54 Speech White Amolitude Mix 5 50 Soliton Ton A Sol Mix 5 57 Speech Freedom Of Speech Mix 8 00 Melt Mr Babbit Mix 7 30 Speech Speechless Mix 9 32 References http www.pitchblack.co.nz ?s1 albums&s2 futureproof Futureproof on Pitch Black s official site http www.discogs.com Pitch Black Futureproof release 66586 Futureproof on discogs.com Category Pitch Black albums Category 1999 debut albums Category Debut albums 1990s electronic album stub ... more details
of soliton solutions. Origin of the equation and its name There are two equivalent forms of the sine ... n 2 infty frac varphi 2 n 2n . end align math Soliton solutions An interesting feature of the sine Gordon equation is the existence of soliton and multisoliton solutions. 1 soliton solutions The sine Gordon equation has the following 1 soliton solutions math varphi text soliton x, t 4 arctan e m gamma x v t delta , math where math gamma 2 frac 1 1 v 2 . math The 1 soliton solution for which we have ... as they are constant solutions of zero energy. The 1 soliton solution in which we take the negative root for math gamma math is called an antikink . The form of the 1 soliton solutions can be obtained ... varphi 2 right text with varphi varphi 0 0 math for all time. The 1 soliton solutions can be visualized .... Image Sine gordon 1.gif frame Traveling kink soliton represents propagating clockwise twist. Image Sine gordon 2.gif frame Traveling antikink soliton represents propagating counterclockwise twist. 2 soliton solutions Multi soliton solutions can be obtained through continued application of the B cklund transform to the 1 soliton solution, as prescribed by a Bianchi lattice relating the transformed ... York Cambridge University Press, 2002. ref The 2 soliton solutions of the sine Gordon equation show ... 4.gif frame Kink kink collision. Another interesting 2 soliton solutions arise from the possibility ... main.html Solitons and Soliton Collisions . ref Image Sine gordon 5.gif frame Standing breather is a swinging in time coupled kink antikink soliton. Image Sine gordon 6.gif frame Large amplitude moving ... has a breather envelope. 3 soliton solutions 3 soliton collisions between a traveling kink ... where math varphi math is now a function of the variables x and y . This is no longer a soliton ... . The particle spectrum consists of a soliton, an anti soliton and a finite possibly zero number of breathers ... more details
cases support breather solutions. Breathers are soliton ic structures. There are two types of breathers ... S. http homepages.tversu.ru s000154 collision main.html Solitons and Soliton Collisions . ref Standing ... , and has soliton solutions. In the de focusing nonlinear Schr dinger equation the nonlinearity parameter ... 2 . Note that a limiting case of the breather solution is the Peregrine soliton ref cite journal last1 ... The Peregrine soliton in nonlinear fibre optics journal Nature Physics doi 10.1038 nphys1740 volume 6 issue 10 bibcode 2010NatPh...6..790K pages 790 ref . See also breather surface soliton References ... more details
to gain analytical insights into non linear equations, and in the process, discovered the soliton ... article Soliton Article on Visiometrics http www.scholarpedia.org article Visiometrics External ... more details
In a single mode optical fiber , the zero dispersion wavelength is the wavelength or wavelengths at which material dispersion optics dispersion and waveguide dispersion cancel one another. In all silica based optical fiber s, minimum material dispersion occurs naturally at a wavelength of approximately 1300nm. Single mode fibers may be made of silica based glasses containing dopants that shift the material dispersion wavelength, and thus, the zero dispersion wavelength, toward the minimum loss window at approximately 1550nm. The engineering tradeoff is a slight increase in the minimum attenuation coefficient . Such fiber is called dispersion shifted fiber . Another way to alter the dispersion is changing the core size and the refractive indices of the material of Fiber optics Principle of operation core and Cladding fiber optics cladding . Because fiber optic materials are already highly optimized for low scattering and high transparency alternative ways to change the refractive index were investigated. As a straight forward solution tapered fiber s and holey fiber s or photonic crystal fiber s PCF were produced. Essentially they replace the cladding by air. This improves the contrast of refractive indices by a factor of 10. Therefore the effective index is changed, especially for longer wavelengths. This type of refractive index change versus wavelength due to different geometry is called waveguide dispersion . As these narrow waveguides 1 3 m core diameter are combined with ultrashort pulse s at the zero dispersion wavelength pulses are not instantly destroyed by dispersion. After reaching a certain peak power within the pulse the non linear refractive index starts to play an important role leading to frequency generation processes like self phase modulation SPM , modulational instability , soliton optics soliton generation and soliton fission , cross phase modulation XPM and others. All these processes generate new frequency components, meaning that narrow ... more details
Summary Space time plot of a breathing dissipative soliton in a two component reaction diffusion system, generated by Dr. Hendrik U. Boedeker June 2007 . The system reads math begin array rl partial t u & d u 2 Delta u lambda u u 3 kappa 3 v kappa 1, tau partial t v & d v 2 Delta v u v end array math with &lambda 4.67, &tau 5.0, d sub u sub sup 2 sup 0.000467, d sub v sub sup 2 sup 0.01, &kappa sub 1 sub 1.126, &kappa sub 3 sub 3.33, no flux boundary conditions have been used. A finite element algorithm was used in the calculation. Licensing self GFDL cc by sa 2.5,2.0,1.0 migration relicense Copy to Wikimedia Commons bot Fbot priority true ... more details
Summary Stationary dissipative soliton numerical calculation in a two component reaction diffusion system of Fitzhugh Nagumo type, produced by Dr. H. U. B deker. The system reads math begin array rl partial t u & d u 2 Delta u lambda u u 3 sigma v kappa, tau partial t v & d v 2 Delta v u v end array math with &lambda 4.67, &sigma 3.33, &tau 0.1, d sub u sub sup 2 sup 0.004, d sub v sub sup 2 sup 0.01, &kappa 1. The solution was found by starting with a Gaussian initial distribution in u and calculating the temporal evolution with a finite element algorithm. Licensing self GFDL cc by sa 2.5,2.0,1.0 migration relicense Copy to Wikimedia Commons bot Fbot priority true ... more details
In the theory of integrable systems , a compacton , introduced in harvs last1 Rosenau first1 Philip last2 Hyman first2 James M. title Compactons Solitons with finite wavelength publisher American Physical Society year 1993 journal Physical Review Letters volume 70 issue 5 pages 564 567 , is a soliton with Compact support Compact support compact support . An example of an equation with compacton solutions is the generalization math u t u m x u n xxx 0 , math of the Korteweg de Vries equation with m , n 1. The case when m 2, n 1 is essentially the KdV equation. Example The equation math u t u 2 x u 2 xxx 0 , math has a travelling wave solution given by math u x,t begin cases dfrac 4 lambda 3 cos 2 x lambda t 4 & text if x lambda t le 2 pi, 0 & text if x lambda t ge 2 pi. end cases math This has compact support in x , so is a compacton. See also peakon vector soliton References citation url http www.ams.org notices 200507 what is.pdf title What is a compacton? last1 Rosenau first1 Philip journal Notices of the A. M. S. year 2005 pages 738 739 Citation last1 Rosenau first1 Philip last2 Hyman first2 James M. title Compactons Solitons with finite wavelength publisher American Physical Society year 1993 journal Physical Review Letters volume 70 issue 5 pages 564 567 doi 10.1103 PhysRevLett.70.564 bibcode 1993PhRvL..70..564R Category Solitons ... more details
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