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 partial differential equation combining the purely nonlinear convective term with the purely nonlinear reactive term. The obtained global and blow-up solutions, which might be used in the further numerical and analytical analyses of such models, are illustrated with suitable parameters.
Highlights
This study focuses on the travelling wave solutions of a newly introduced dispersion-convection-reaction model ( ) ut + unux + uxxx = ru 1− un, (1)where n 0, is a parameter for the purely nonlinear convection term, is a parameter for the linear dispersion term and r is a parameter for the purely nonlinear reaction term
This paper proposes a new dispersion-convection-reaction model, which is called the generalized KdV (gKdV)-Fisher equation, to obtain the travelling wave solutions by using the Riccati equation method
We use the Riccati equation method [27-36] to reveal the travelling wave solutions of the gKdV-Fisher equation, which are the cooperative results of the proposed combined model
Summary
This study focuses on the travelling wave solutions of a newly introduced dispersion-convection-reaction model ( ) ut + unux + uxxx = ru 1− un ,. The exact travelling waves of the KdV-Burgers-Fisher equation ut + uux − uxx + uxxx = ru (1− u) ,. We would like to remind the neighbouring nonlinear parabolic equation, which is a diffusionconvection-reaction model and called the generalized Burgers-Fisher equation [25,26],. We use the Riccati equation method [27-36] to reveal the travelling wave solutions of the gKdV-Fisher equation, which are the cooperative results of the proposed combined model. It is reasonable to expect kink and antikink wave solutions because of the reaction term in the proposed equation
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