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

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.

Keywords

• Reaction–diffusion
• Time delay
• Exact solutions
• Differential equations