Results 11 to 20 of about 605 (73)
East Asian Journal on Applied Mathematics, 2019 The (3 + 1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation is studied by using the Hirota bilinear method and the graphical representations of the solutions.
Ding Guo +3 more
semanticscholar +1 more source
(Non)linear instability of periodic traveling waves: Klein–Gordon and KdV type equations
Advances in Nonlinear Analysis, 2014 We prove the existence and nonlinear instability of periodic traveling wave solutions for the critical one-dimensional Klein–Gordon equation. We also establish a linear instability criterium for a KdV type system.
Angulo Pava Jaime, Natali Fabio
doaj +1 more source
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
wiley +1 more source
Andrew Lenard: A Mystery Unraveled [PDF]
, 2005 The theory of bi-Hamiltonian systems has its roots in what is commonly referred to as the "Lenard recursion formula". The story about the discovery of the formula told by Andrew Lenard is the subject of this article.Comment: Published in SIGMA (Symmetry,
Praught, Jeffery, Smirnov, Roman G.
core +2 more sources
Painleve analysis of a class of nonlinear diffusion equations
International Journal of Stochastic Analysis, Volume 9, Issue 1, Page 77-86, 1996., 1995 We study the Painleve analysis for a class of nonlinear diffusion equations. We find that in some cases it has only the conditional Painleve property and in other cases, just the Painleve property. We also obtained special solutions.
P. Chandrasekaran, E. K. Ramasami
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
Localized Induction Equation for Stretched Vortex Filament [PDF]
, 2006 We study numerically the motion of the stretched vortex filaments by using the localized induction equation with the stretch and that without the stretch.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at ...
Kakuhata, Hiroshi, Konno, Kimiaki
core +4 more sources
Restricted Flows and the Soliton Equation with Self-Consistent Sources [PDF]
, 2006 The KdV equation is used as an example to illustrate the relation between the restricted flows and the soliton equation with self-consistent sources. Inspired by the results on the Backlund transformation for the restricted flows (by V.B. Kuznetsov et al.
Lin, Runliang, Yao, Haishen, Zeng, Yunbo
core +4 more sources
, 2013 In this paper, we propose a new fractional sub-equation method for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative, which is the fractional version of the known (G′/G ...
B. Zheng, Chuanbao Wen
semanticscholar +1 more source
Multi-soliton Solutions of Two-dimensional Matrix Davey-Stewartson Equation [PDF]
, 1996 The explicit formulae for m-soliton solutions of (1+2)-dimensional matrix Davey-Stewartson equation are represented. They are found by means of known general solution of the matrix Toda chain with the fixed ends [1].
A.N. Leznov +15 more
core +3 more sources