Abstract
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.
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