Soliton-like solutions to the generalized Burgers-Huxley equation with variable coefficients

Abstract

In this paper, we consider the generalized Burgers-Huxley equation with arbitrary power of nonlinearity and timedependent coefficients. We analyze the traveling wave problem and explicitly find new soliton-like solutions for this extended equation by using the ansatz of Zhao et al. [X. Zhao, D. Tang, L. Wang, Phys. Lett. A 346 (2005) 288–291]. We also employ the solitary wave ansatz method to derive the exact bright and dark soliton solutions for the considered evolution equation. The physical parameters in the soliton solutions are obtained as function of the time-dependent model coefficients. The conditions of existence of solitons are presented. As a result, rich exact travelling wave solutions, which contain new soliton-like solutions, bell-shaped solitons and kink-shaped solitons for the generalized Burgers-Huxley equation with time-dependent coefficients, are obtained. The methods employed here can also be used to solve a large class of nonlinear evolution equations with variable coefficients.