Overtaking collisions of m shock waves and interactions of n(n→∞)-lump, m(m→∞)-solitons, τ(τ→∞)-periodic waves solutions to a generalized (2+1)-dimensional new KdV model

Abstract

We consider a new generalized (2+1)-dimensional KdV model to investigate m ( m → ∞ ) shock and n ( n → ∞ ) breather wave solutions via two integral schemes. For the treatment of the model in an auxiliary equation approach, we first convert a nonlinear Burger equation to an ordinary differential equation (ODE) through a certain transformation. This ODE is used as an auxiliary equation of the method to obtain m ( m → ∞ ) shock wave solutions of the model. For different values of the parameters, we present head on and overtaking collisions with scattering ways of particle of the m ( m → ∞ ) shock wave solutions. We construct n soliton solutions of the model by using Hirota-bilinear approach. We obtain one lump type breather waves, interactions of one breather wave with a kink wave, interactions of two lump type breather waves by choosing complex conjugate values of free parameters in the n -soliton solutions of the model. Finally, we introduce two lemmas, a theorem and few corollaries on the hybrid interaction ( n → ∞ lumps, m → ∞ solitons and τ → ∞ periodic waves) solutions of the model. The theories and results are illustrated with adequate examples and suitable graphs. • We propose a generalized (2+1)- dimensional new KdV model for investigation waves solutions. • Derive m (m → ∞ ) shock wave solutions of the model. • Present head on and overtaking collisions with scattering ways of particle of the m (m → ∞ ) shock wave solutions. • We introduce two lemmas, a theorem and few corollaries on the hybrid interaction (n → ∞ lumps, m → ∞ solitons and τ → ∞ periodic waves) solutions of the model. • The theories and results are illustrated with adequate examples and suitable graphs.