Traveling waves in nonlinear media with dispersion, dissipation, and reaction

Abstract

The traveling wave solutions of the newly proposed KdV–Burgers–Fisher equation, which is a dispersion–dissipation–reaction model, are investigated with the appropriate parameters. Moreover, in this paper, the new solitary wave solutions of an extended fifth-order model equation are revealed. Using one of the efficient symbolic computations, we obtain the cooperative interactions, such as soliton, anti-soliton, kink, and anti-kink wave solutions, and illustrate the long-time behavior. We believe that the proposed equations with their wave solutions can accelerate the further studies for physical and engineering models combining the different entities, such as dispersion, diffusion, convection, reaction, and nonlinearity.