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 (q"t+(q^2)"x+(q^2)"x"x"t)"x+q"y"y=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 lim"@x"->"+/-"~q(@x)=A 0, or possesses compacton solutions only when lim"@x"->"+/-"~q(@x)=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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