Single peak solitary wave solutions for the generalized KP-MEW (2, 2) equation under boundary condition

The qualitative theory of differential equations is applied to the KP-MEW (2, 2) equation (qt+(q2)x+(q2)xxt)x+qyy=0. Our procedure shows that the KP-MEW (2, 2) equation either has the regular peakon soliton, cuspon soliton and smooth soliton solutions when sitting on the non-zero constant pedestal limξ→±∞q(ξ)=A≠0, or possesses compacton solutions only when limξ→±∞q(ξ)=A=0. In particular, we present mathematical analysis and numerical simulations are provided for those peakon, cuspon, compacton, loop soliton and smooth soliton solutions.