Results 31 to 40 of about 1,267 (106)
Higher‐order KdV‐type equations and their stability
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 4, Page 215-220, 2001., 2001 We have derived solitary wave solutions of generalized KdV‐type equations of fifth order in terms of certain hyperbolic functions and investigated their stability. It has been found that the introduction of more dispersive effects increases the stability range.
E. V. Krishnan, Q. J. A. Khan
wiley +1 more source
Higher-Order Rogue Wave and Rational Soliton Solutions of Discrete Complex mKdV Equations
East Asian Journal on Applied Mathematics, 2018 The generalised perturbation (n, N − n)-fold Darboux transformation is used to derive new higher-order rogue wave and rational soliton solutions of the discrete complex mKdV equations.
Xiaoyong Wen
semanticscholar +1 more source
An explicit solution of coupled viscous Burgers′ equation by the decomposition method
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 11, Page 675-680, 2001., 2001 We consider a coupled system of viscous Burgers′ equations with appropriate initial values using the decomposition method. In this method, the solution is calculated in the form of a convergent power series with easily computable components. The method does not need linearization, weak nonlinearity assumptions or perturbation theory.
Doğan Kaya
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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
doaj +1 more source
On Transformations of the Rabelo Equations [PDF]
, 2007 We study four distinct second-order nonlinear equations of Rabelo which describe pseudospherical surfaces. By transforming these equations to the constant-characteristic form we relate them to some well-studied integrable equations.
Sakovich, Anton, Sakovich, Sergei
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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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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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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
wiley +1 more source
Multipeakons and a theorem of Stieltjes
, 1999 A closed form of the multi-peakon solutions of the Camassa-Holm equation is found using a theorem of Stieltjes on continued fractions.
Beals R +6 more
core +2 more sources
One-dimensional weakly nonlinear model equations for Rossby waves [PDF]
, 2014 In this study we explore several possibilities for modelling weakly nonlinear Rossby waves in fluid of constant depth, which propagate predominantly in one direction.
Henry, David, Ivanov, Rossen
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