Exp-function method for solving the Burgers-Fisher equation with variable coefficients

In this paper, the exp-function method with the aid of symbolic computational system is used to obtain generalized travelling wave solutions of a Burgers-Fisher equation with variable coefficients. It is shown that the exp-function method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool to solve the nonlinear evolution equation with variable coefficients in mathematical physics.

💡 Research Summary

The paper presents a systematic application of the exp‑function method, assisted by symbolic computation software, to obtain generalized travelling‑wave solutions of the Burgers‑Fisher equation when its coefficients are functions of space and/or time. The authors begin by highlighting the importance of the Burgers‑Fisher equation in modelling combined diffusion, convection, and reaction processes, and they note that while the constant‑coefficient version has been extensively studied with a variety of analytical techniques, the variable‑coefficient case remains largely intractable analytically and is usually tackled by numerical methods.

To address this gap, the authors first perform a travelling‑wave reduction. Introducing the similarity variable
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