Mixed Equilibrium Problems and Anti-periodic Solutions for Nonlinear Evolution Equations

2015 ◽  
Vol 168 (2) ◽  
pp. 410-440 ◽  
Author(s):  
Ouayl Chadli ◽  
Qamrul Hasan Ansari ◽  
Jen-Chih Yao
Keyword(s):  
Periodic Solutions ◽  
Evolution Equations ◽  
Equilibrium Problems ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium

Jacobi Elliptic Function Rational Expansion Method with Symbolic Computation to Construct New Doubly-periodic Solutions of Nonlinear Evolution Equations

2004 ◽  
Vol 59 (9) ◽  
pp. 529-536 ◽  
Author(s):  
Yong Chen ◽  
Qi Wang ◽  
Biao Lic
Keyword(s):  
Periodic Solutions ◽  
Symbolic Computation ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Jacobi Elliptic Function ◽  
Rational Form

A new Jacobi elliptic function rational expansion method is presented by means of a new general ansatz and is very powerful, with aid of symbolic computation, to uniformly construct more new exact doubly-periodic solutions in terms of rational form Jacobi elliptic function of nonlinear evolution equations (NLEEs). We choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we obtain the solutions found by most existing Jacobi elliptic function expansion methods and find other new and more general solutions at the same time. When the modulus of the Jacobi elliptic functions m→1 or 0, the corresponding solitary wave solutions and trigonometric function (singly periodic) solutions are also found.

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