Compacton, peakon, cuspons, loop solutions and smooth solitons for the generalized KP–MEW equation

In this paper, we investigate all possible single traveling solitary wave solutions of the generalized KP–MEW equation (ut−(u2)x−(u2)xxt)x−uyy=0(ut−(u2)x−(u2)xxt)x−uyy=0 under boundary condition limξ→±∞u(ξ)=Alimξ→±∞u(ξ)=A. Regular compacton solution of the generalized KP–MEW equation correspond to the case of A=0A=0. In the case of A≠0A≠0, we find new exact soliton solutions including loop solution, cusped soliton, peaked soliton and smooth soliton solutions. The parametric conditions of existence of the loop solution, cusped soliton, peaked soliton, smooth soliton and compacton solutions are given by using the phase portrait analytical technique. Mathematical analysis and numerical simulations are provided for these soliton solutions of the generalized KP–MEW equation. We show some graphs to explain these solutions.