Extended Tanh-Function Method and Its Applications in Nonlocal Complex mKdV Equations

In order to construct the multiple traveling wave solutions of the nonlocal modified Korteweg de Vires (mKdV) equation, the modified tanh-function approach for local soliton equations is extended to a nonlocal complex mKdV equation. The central idea of this method is to use the solution of the Riccati equation to replace the tanh function in the tanh function (THF) method. As an application, we investigate a new traveling wave solution for the nonlocal complex mKdV equation of Ablowitz and Musslimani. Moreover, some exciting diagrams show the underlying dynamics of some given solutions.

Automated summary

This study extends the modified tanh-function approach for local soliton equations to a nonlocal complex mKdV equation, using the solution of the Riccati equation to replace the tanh function. It explores new traveling wave solutions for the nonlocal complex mKdV equation and presents exciting diagrams showing the dynamics of given solutions.