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

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.