Explicit and Exact Traveling Wave Solutions of Cahn Allen equation using MSE Method

TL;DR

This paper employs the Modified Simple Equation (MSE) method to derive explicit traveling wave solutions of the Cahn-Allen equation, demonstrating its applicability in various scientific fields.

Contribution

It introduces the use of the MSE method to find exact solitary wave solutions of the Cahn-Allen equation, expanding analytical tools for this nonlinear PDE.

Findings

Existence of solitary wave solutions confirmed.

Explicit hyperbolic solutions characterized with free parameters.

Graphical analysis illustrates solution dynamics.

Abstract

By using Modified simple equation method, we study the Cahn Allen equation which arises in many scientific applications such as mathematical biology, quantum mechanics and plasma physics. As a result, the existence of solitary wave solutions of the Cahn Allen equation is obtained. Exact explicit solutions interms of hyperbolic solutions of the associated Cahn Allen equation are characterized with some free parameters. Finally, the variety of structure and graphical representation make the dynamics of the equations visible and provides the mathematical foundation in mathematical biology, quantum mechanics and plasma physics.