Exact solutions for the third-order dispersive-Fisher equations

Abstract

In this study, we reveal the exact solutions of the third-order semilinear and nonlinear dispersive equations containing Fisher-like nonlinearity, i.e. dispersion-reaction models, which can be used in physical and engineering applications, such as fibre optics, communication theory and transport in porous media. The variants of auxiliary equation method, which are based on Mathieu, Bernoulli and classical Riccati equations, are used for these equations. Obtained solutions are discussed and illustrated in details. Although studies on the third-order equations have been intriguing for many years, the proposed equations were not studied in the literature. We believe that the proposed results will be key part of further analytical and numerical studies for waves in the dispersive medium with reaction.