2021•Maǧallaẗ ǧāmiʿaẗ al-Sulṭān Qābūs li-l-ʿulūm/Sultan Qaboos University journal for scienceOpen access

Travelling Wave Solutions for Fisher’s Equation Using the Extended Homogeneous Balance Method

Mohammad M. Fares, Usama M. Abdelsalam, Faiza M. Allehiany

Abstract

In this work, the extended homogeneous balance method is used to derive exact solutions of nonlinear evolution equations. With the aid of symbolic computation, many new exact travelling wave solutions have been obtained for Fisher’s equation and Burgers-Fisher equation. Fisher’s equation has been widely used in studying the population for various systems, especially in biology, while Burgers-Fisher equation has many physical applications such as in gas dynamics and fluid mechanics. The method used can be applied to obtain multiple travelling wave solutions for nonlinear partial differential equations.

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Key concepts: Fisher equation, Fisher's equation, Burgers' equation, Partial differential equation, Mathematics, Nonlinear system, Population balance equation, Exact differential equation