Nonlinear wave solution to a coupled mKdV equations with variable coefficients

TL;DR

This paper derives various nonlinear wave solutions for coupled mKdV equations with variable coefficients using the F-expansion method, including elliptic, torsional, periodic, and solitary waves.

Contribution

It introduces a systematic approach to find multiple types of solutions for coupled mKdV equations with variable coefficients, expanding the solution set beyond existing methods.

Findings

12 Jacobi elliptic function solutions identified

Torsional, periodic, and solitary wave solutions derived in limit cases

Method demonstrates effectiveness for variable coefficient coupled equations

Abstract

The nonlinear wave solutions to coupled mKdV equations with variable coefficients are obtained by using the F-expansion method, including 12 kinds of Jacobi elliptic function solutions. In the limit cases, the torsional wave solutions, periodic solutions and solitary wave solutions are obtained as well.