Rational Jacobi elliptic solutions for nonlinear differential–difference lattice equations

Exact Solutions for Nonlinear Evolution Equations with Jacobi Elliptic Function Rational Expansion Method

In this paper we implement the unified rational expansion methods, which leads to find exact rational formal polynomial solutions of nonlinear partial differential equations (NLPDEs), to the (1+1)dimensional dispersive long wave and Clannish Random Walker’s parabolic (CRWP) equations. By using this scheme, we get some solutions of the (1+1)-dimensional dispersive long wave and CRWP equations in...

The Modified Rational Jacobi Elliptic Functions Method for Nonlinear Differential Difference Equations

We modified the rational Jacobi elliptic functions method to construct some new exact solutions for nonlinear differential difference equations in mathematical physics via the lattice equation, the discrete nonlinear Schrodinger equation with a saturable nonlinearity, the discrete nonlinear Klein-Gordon equation, and the quintic discrete nonlinear Schrodinger equation. Some new types of the Jac...

New Jacobi Elliptic Function Solutions for the Zakharov Equations

New Explicit Jacobi Elliptic Function Solutions for the Zakharov Equations ⋆

In this letter, some new complex doubly periodic solutions to the Zakharov equations are obtained by using the generalized Jacobi elliptic function expansion method with the aid of mathematica software, some of which are degenerated to the solitary wave solutions and the triangle function solutions in the limit cases when the modulus of the Jacobian elliptic functions m→1 or 0, which shows that...

Existence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weight

‎This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight‎. ‎We apply the variational methods to prove the existence of ground state solution‎.