Equivalent of the elliptic function solutions of nonlinear differential equations

TL;DR

This paper demonstrates that many Jacobi elliptic function solutions to nonlinear differential equations are equivalent through modulus and phase transformations, using the mKdV equation as an example.

Contribution

It reveals the equivalence of elliptic function solutions via transformations, clarifying the structure of solutions to nonlinear differential equations.

Findings

Many solutions are equivalent through transformations

Jacobi elliptic functions can be transformed into each other

Application to the mKdV equation confirms the theory

Abstract

In this paper, we point out that many Jacobi elliptic function solutions to non-linear differential equation(NDE) can be transformed each other via the modulus and phase transformation of Jacobi elliptic function. Therefore these solutions are equivalent. We investigate equivalent of the Jacobi elliptic function solutions of Korteweg-de Vries (mKdV) equation as a example.