Exact solutions of nonlinear delay reaction-diffusion equations with variable coefficients

TL;DR

This paper introduces a novel method to derive exact traveling-wave solutions for nonlinear delay reaction-diffusion equations with variable coefficients, enhancing analytical tools for complex PDEs.

Contribution

A new technique using functional constraints is developed to find exact solutions of generalized nonlinear delay reaction-diffusion equations with variable coefficients.

Findings

Exact traveling-wave solutions with arbitrary functions and free parameters obtained.

Method applicable to more complex partial differential equations.

Solutions demonstrated with specific examples and graphical representations.

Abstract

A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized form of nonlinear equations of reaction-diffusion type with delay and which are nonlinear and associated with variable coefficients. A novel technique is used in this study to obtain the exact solutions which are new and are of the form of traveling-wave solutions. Arbitrary functions are present in the solutions and they also contain free parameters, which make them suitable for usage in solving certain modeling problems, testing numerical and approximate analytical methods. The results of this study also find applications in obtaining the exact solutions of other forms of partial differential equations which are more complex. Specific examples of nonlinear equations of reaction-diffusion type with delay are given and their exact solutions are presented. Solutions of certain reaction-diffusion equations are also displayed graphically.