Solitons and periodic solutions to a couple of fractional nonlinear evolution equations

Pramana ◽  
2014 ◽  
Vol 82 (3) ◽  
pp. 465-476 ◽  
Author(s):  
M MIRZAZADEH ◽  
M Eslami ◽  
ANJAN BISWAS
Keyword(s):  
Periodic Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations

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.

Periodic Solutions for Nonlinear Evolution Equations in RN

2013 ◽  
Vol 860-863 ◽  
pp. 2830-2833
Author(s):  
Li Hong Zhang ◽  
Wei Jie Li
Keyword(s):  
Linear Operator ◽  
Periodic Solutions ◽  
Bounded Linear Operator ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Periodic Problem ◽  
Nonlinear Evolution Equations ◽  
Bounded Linear

The aim of this paper is to establish the existence and uniqueness of periodic solutions for a nonlinear periodic problem: in RN where A(t, x) is a nonlinear map and B is a bounded linear operator from RNto RN .

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