Single peak solitary wave solutions for the CH-KP(2,1) equation under boundary condition

• The qualitative theory of differential equations is applied to the CH-KP(2,1) equation.
• The existence of the regular loop soliton, peakon, cuspon, compacton and smooth soliton solutions when sitting on the constant pedestal limx,y→±∞⁡u(x,y)=Alimx,y→±∞⁡u(x,y)=A is proved.
• Some new types of loop soliton, cusped soliton, peaked soliton, smooth soliton and compacton solutions, which are given in explicit forms.

The qualitative theory of differential equations is applied to the CH-KP(2,1) equation [ut+2ux−(u2)xxt−uux]x+uyy=0[ut+2ux−(u2)xxt−uux]x+uyy=0. Our procedure shows that the CH-KP(2,1) equation either has the regular peakon soliton, cuspon soliton and smooth soliton solutions when sitting on the non-zero constant pedestal limx→±∞⁡u=A≠0limx→±∞⁡u=A≠0, or possesses compacton solutions only when limx→±∞⁡u=A=0limx→±∞⁡u=A=0. In particular, mathematical analysis and numerical simulations of the CH-KP(2,1) equation are provided for those peakon, cuspon, compacton, loop soliton and smooth soliton solutions.