scholarly journals Solitons for a (2+1)-dimensional Sawada–Kotera equation via the Wronskian technique

2017 ◽  
Vol 74 ◽  
pp. 193-198 ◽  
Author(s):  
Shu-Liang Jia ◽  
Yi-Tian Gao ◽  
Cui-Cui Ding ◽  
Gao-Fu Deng
Keyword(s):  
Wronskian Technique

scholarly journals Two Different Classes of Wronskian Conditions to a (3 + 1)-Dimensional Generalized Shallow Water Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Yaning Tang ◽  
Pengpeng Su
Keyword(s):  
Shallow Water ◽  
Shallow Water Equation ◽  
Sufficient Conditions ◽  
Wronskian Technique ◽  
Rational Solutions ◽  
Bilinear Method ◽  
Wronskian Determinant ◽  
Linear Partial Differential Equations ◽  
Hirota Bilinear Equation ◽  
Hirota Bilinear

Based on the Hirota bilinear method and Wronskian technique, two different classes of sufficient conditions consisting of linear partial differential equations system are presented, which guarantee that the Wronskian determinant is a solution to the corresponding Hirota bilinear equation of a (3+1)-dimensional generalized shallow water equation. Our results show that the nonlinear equation possesses rich and diverse exact solutions such as rational solutions, solitons, negatons, and positons.

Soliton solutions of the Korteweg de Vries and the Kadomtsev-Petviashvili equations: the Wronskian technique

1983 ◽  
Vol 389 (1797) ◽  
pp. 319-329 ◽  
Keyword(s):  
Evolution Equation ◽  
Soliton Solution ◽  
Soliton Solutions ◽  
Inverse Scattering Method ◽  
Compact Representation ◽  
Scattering Method ◽  
Wronskian Technique ◽  
Hirota Bilinear Form ◽  
Usual Representation ◽  
Hirota Bilinear

The well known soliton solutions of the Kadomtsev-Petviashvili equations are written in terms of determinants of Wronskian form. By using this compact representation together with the Hirota bilinear form of the equations, it is demonstrated by elementary algebraic methods that the N -soliton solution satisfies the evolution equation and the N and N + 1-soliton solutions satisfy the associated Bäcklund transformation. The relation of these results to the eigensolutions of the inverse scattering method and to the more usual representation of the N -soliton solution is also given.

N-SOLITON-LIKE SOLUTIONS AND BÄCKLUND TRANSFORMATIONS FOR A NON-ISOSPECTRAL AND VARIABLE-COEFFICIENT MODIFIED KORTEWEG-DE VRIES EQUATION

2011 ◽  
Vol 25 (05) ◽  
pp. 723-733 ◽  
Author(s):  
QIAN FENG ◽  
YI-TIAN GAO ◽  
XIANG-HUA MENG ◽  
XIN YU ◽  
ZHI-YUAN SUN ◽  
...  
Keyword(s):  
Variable Coefficient ◽  
Vries Equation ◽  
Bäcklund Transformation ◽  
Lax Pair ◽  
Mkdv Equation ◽  
Wronskian Technique ◽  
Backlund Transformation ◽  
Bilinear Bäcklund Transformation ◽  
De Vries ◽  
Bilinear Equations

A non-isospectral and variable-coefficient modified Korteweg–de Vries (mKdV) equation is investigated in this paper. Starting from the Ablowitz–Kaup–Newell–Segur procedure, the Lax pair is established and the Bäcklund transformation in original variables is also derived. By a dependent variable transformation, the non-isospectral and variable-coefficient mKdV equation is transformed into bilinear equations, by virtue of which the N-soliton-like solution is obtained. In addition, the bilinear Bäcklund transformation gives a one-soliton-like solution from a vacuum one. Furthermore, the N-soliton-like solution in the Wronskian form is constructed and verified via the Wronskian technique.

scholarly journals New Exact Solutions for the (3+1)-Dimensional Generalized BKP Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Jun Su ◽  
Genjiu Xu
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
Wronskian Technique ◽  
Rational Solutions ◽  
Wronskian Determinant ◽  
New Exact Solutions ◽  
Positon Solutions ◽  
Bkp Equation

The Wronskian technique is used to investigate a (3+1)-dimensional generalized BKP equation. Based on Hirota’s bilinear form, new exact solutions including rational solutions, soliton solutions, positon solutions, negaton solutions, and their interaction solutions are formally derived. Moreover we analyze the strangely mechanical behavior of the Wronskian determinant solutions. The study of these solutions will enrich the variety of the dynamics of the nonlinear evolution equations.

The triple Wronskian solutions to the variable-coefficient Manakov model

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640031
Author(s):  
Yi Zhang ◽  
Kun Ma
Keyword(s):  
Bilinear Form ◽  
Variable Coefficient ◽  
Wronskian Technique ◽  
Manakov Model

In this paper, the variable-coefficient Manakov model whose bilinear form exists is mainly discussed. Based on the Wronskian technique, the triple Wronskian form solutions are obtained and the interactions between the two solitons are investigated.

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