Kink and anti-kink wave solutions for the generalized KdV equation withFisher-type nonlinearity

Abstract

This paper proposes a new dispersion-convection-reaction model, which is called the gKdV-Fisher equation, to obtain the travelling wave solutions by using the Riccati equation method. The proposed equation is a third-order dispersive partialdifferential equation combining the purely nonlinear convective term with thepurely nonlinear reactive term. The obtained global and blow-up solutions, whichmight be used in the further numerical and analytical analyses of such models, areillustrated with suitable parameters.