CTE Solvability, Nonlocal Symmetries and Exact Solutions of Dispersive Water Wave System

2014 ◽  
Vol 61 (5) ◽  
pp. 545-550 ◽  
Author(s):  
Chun-Li Chen ◽  
Sen-Yue Lou
Keyword(s):  
Exact Solutions ◽  
Water Wave ◽  
Wave System ◽  
Nonlocal Symmetries

New Exact Solutions and Localized Excitations in a (2+1)-Dimensional Soliton System

2009 ◽  
Vol 64 (1-2) ◽  
pp. 37-43
Author(s):  
Song-Hua Ma ◽  
Jian-Ping Fang
Keyword(s):  
Exact Solutions ◽  
Water Wave ◽  
Reduction Method ◽  
Wave System ◽  
Similarity Reduction ◽  
New Exact Solutions ◽  
Localized Excitations ◽  
Reduction Equation ◽  
Dimensional Soliton

Starting from a special conditional similarity reduction method, we obtain the reduction equation of the (2+1)-dimensional dispersive long-water wave system. Based on the reduction equation, some new exact solutions and abundant localized excitations are obtained.

New Exact Solutions for Two Nonlinear Equations

2006 ◽  
Vol 61 (1-2) ◽  
pp. 1-6 ◽  
Author(s):  
Zonghang Yang
Keyword(s):  
Wave Equation ◽  
Partial Differential Equations ◽  
Exact Solutions ◽  
Water Wave ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
New Exact Solutions ◽  
Complex Phenomena ◽  
Sivashinsky Equation

Nonlinear partial differential equations are widely used to describe complex phenomena in various fields of science, for example the Korteweg-de Vries-Kuramoto-Sivashinsky equation (KdV-KS equation) and the Ablowitz-Kaup-Newell-Segur shallow water wave equation (AKNS-SWW equation). To our knowledge the exact solutions for the first equation were still not obtained and the obtained exact solutions for the second were just N-soliton solutions. In this paper we present kinds of new exact solutions by using the extended tanh-function method.

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