Abstract
The qualitative theory of differential equations is applied to the CH-KP(2,1) equation [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≠0, or possesses compacton solutions only when limx→±∞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.
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