scholarly journals The classification of the single traveling wave solutions to ( 1 + 1 ) $(1+1)$ dimensional Gardner equation with variable coefficients

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Damin Cao ◽  
Lijuan Du
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Variable Coefficients ◽  
Gardner Equation ◽  
Wave Solutions

THE EXACT TRAVELING WAVE SOLUTIONS AND THEIR BIFURCATIONS IN THE GARDNER AND GARDNER–KP EQUATIONS

2012 ◽  
Vol 22 (05) ◽  
pp. 1250126 ◽  
Author(s):  
FANG YAN ◽  
CUNCAI HUA ◽  
HAIHONG LIU ◽  
ZENGRONG LIU
Keyword(s):  
Traveling Wave ◽  
Function Method ◽  
Traveling Wave Solutions ◽  
Analytic Solutions ◽  
Auxiliary Function ◽  
Kp Equation ◽  
Gardner Equation ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Kp Equations

By using the method of dynamical systems, this paper studies the exact traveling wave solutions and their bifurcations in the Gardner equation. Exact parametric representations of all wave solutions as well as the explicit analytic solutions are given. Moreover, several series of exact traveling wave solutions of the Gardner–KP equation are obtained via an auxiliary function method.

CLASSIFICATION OF ALL ENVELOPE TRAVELING WAVE SOLUTIONS TO (2+1)-DIMENSIONAL DAVEY–STEWARTSON EQUATION

2010 ◽  
Vol 24 (03) ◽  
pp. 363-368 ◽  
Author(s):  
YANG SHU
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Polynomial Method ◽  
Wave Solutions ◽  
Complete Discrimination System

Using the complete discrimination system for polynomial method, we study the (2+1)-dimensional Davey–Stewartson equation and obtain the classifications of all its envelope traveling wave solutions. This is very convenient in practice to give the corresponding solutions for the concrete parameters.

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