Results 31 to 40 of about 1,094 (76)
Periodic and Solitary Wave Solutions for the One-Dimensional Cubic Nonlinear Schrödinger Model
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 Using a similar approach as Korteweg and de Vries, [19], we obtain periodic solutions expressed in terms of the Jacobi elliptic function cn, [3], for the self-focusing and defocusing one-dimensional cubic nonlinear Schrödinger equations.
Bica Ion, Mucalica Ana
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Nonclassical Approximate Symmetries of Evolution Equations with a Small Parameter [PDF]
, 2006 We introduce a method of approximate nonclassical Lie-B\"acklund symmetries for partial differential equations with a small parameter and discuss applications of this method to finding of approximate solutions both integrable and nonintegrable equations ...
Kordyukova, Svetlana
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p‐adic difference‐difference Lotka‐Volterra equation and ultra‐discrete limit
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 4, Page 251-260, 2001., 2001 We study the difference‐difference Lotka‐Volterra equations in p‐adic number space and its p‐adic valuation version. We point out that the structure of the space given by taking the ultra‐discrete limit is the same as that of the p‐adic valuation space. Since ultra‐discrete limit can be regarded as a classical limit of a quantum object, it implies that
Shigeki Matsutani
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Explicit solutions of generalized nonlinear Boussinesq equations
Journal of Applied Mathematics, Volume 1, Issue 1, Page 29-37, 2001., 2001 By considering the Adomian decomposition scheme, we solve a generalized Boussinesq equation. The method does not need linearization or weak nonlinearly assumptions. By using this scheme, the solutions are calculated in the form of a convergent power series with easily computable components.
Doğan Kaya
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The Painleve Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients [PDF]
, 2006 The general KdV equation (gKdV) derived by T. Chou is one of the famous (1+1) dimensional soliton equations with variable coefficients. It is well-known that the gKdV equation is integrable.
Kobayashi, Tadashi, Toda, Kouichi
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Chains of KP, semi‐infinite 1‐Toda lattice hierarchy and Kontsevich integral
Journal of Applied Mathematics, Volume 1, Issue 4, Page 175-193, 2001., 2001 There are well‐known constructions of integrable systems that are chains of infinitely many copies of the equations of the KP hierarchy “glued” together with some additional variables, for example, the modified KP hierarchy. Another interpretation of the latter, in terms of infinite matrices, is called the 1‐Toda lattice hierarchy.
L. A. Dickey
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Gardner's deformations of the Boussinesq equations
, 2006 Using the algebraic method of Gardner's deformations for completely integrable systems, we construct the recurrence relations for densities of the Hamiltonians for the Boussinesq and the Kaup-Boussinesq equations. By extending the Magri schemes for these
Karasu, Atalay, Kiselev, Arthemy V.
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Three‐dimensional Korteweg‐de Vries equation and traveling wave solutions
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 6, Page 379-384, 2000., 2000 The three‐dimensional power Korteweg‐de Vries equation [ut+unux+uxxx] x+uyy+uzz=0, is considered. Solitary wave solutions for any positive integer n and cnoidal wave solutions for n = 1 and n = 2 are obtained. The cnoidal wave solutions are shown to be represented as infinite sums of solitons by using Fourier series expansions and Poisson′s summation ...
Kenneth L. Jones
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Results in Physics, 2016 The propagation of hydrodynamic wave packets and media with negative refractive index is studied in a quintic derivative nonlinear Schrödinger (DNLS) equation.
Chen Yue, Aly Seadawy, Dianchen Lu
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Existence of periodic traveling wave solutions to the generalized forced Boussinesq equation
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 3, Page 643-648, 1999., 1999 The generalized forced Boussinesq equation, utt − uxx + [f(u)]xx + uxxxx = h0, and its periodic traveling wave solutions are considered. Using the transform z = x − ωt, the equation is converted to a nonlinear ordinary differential equation with periodic boundary conditions.
Kenneth L. Jones, Yunkai Chen
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