A note on “Jacobi elliptic function solutions for the modified Korteweg–de Vries equation”

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.

Unbounded Solutions of the Modified Korteweg-De Vries Equation

Abstract We prove local existence and uniqueness of solutions of the focusing modified Korteweg de Vries equation ut+u 2 ux+uxxx = 0 in classes of unbounded functions that admit an asymptotic expansion at infinity in decreasing powers of x. We show that an asymptotic solution differs from a genuine solution by a smooth function that is of Schwartz class with respect to x and that solves a gener...

New Jacobi elliptic function solutions for the double Sine-Gordon equation∗

In this paper, based on the generalized Jacobi elliptic function expansion method,we obtain abundant new complex doubly periodic solutions of the double Sine-Gordon equation (DSGE), which are degenerated to solitary wave solutions and triangle function solutions in the limit cases,showing that this new method is more powerful to seek exact solutions of nonlinear partial differential equations i...

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 the Zakharov Equations