New Jacobi Elliptic Function Solutions for the Zakharov Equations

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...

New Jacobi Elliptic Function Solutions for Coupled KdV-mKdV Equation

A generalized (G ′ /G)-expansion method is used to search for the exact traveling wave solutions of the coupled KdV-mKdV equation. As a result, some new Jacobi elliptic function solutions are obtained. It is shown that the method is straightforward, concise, effective, and can be used for many other nonlinear evolution equations in mathematical physics.

New Exact and Explicit Solutions of the Zakharov Equations and Generalized Zakharov Equations by the Quotient Trigonometric Function Expansion Method

In this work, by using a simple transformation technique, we have show that the nonlinear wave equations: Zakharov equations and generalized Zakharov equations can be reduced to the same family of Duffing or double-well Duffing equations. Then by means of quotient trigonometric function expansion method, many kinds of exact and explicit solutions of this family of equations are obtained in a un...

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...