Special exact soliton solutions for the K(2, 2) equation with non-zero constant pedestal

Abstract Special exact solutions of the K (2, 2) equation, u t  + ( u 2 ) x  + ( u 2 ) xxx  = 0, are investigated by employing the qualitative theory of differential equations. Our procedure shows that the K (2, 2) equation either has loop soliton, cusped soliton and smooth soliton solutions when sitting on the non-zero constant pedestal lim x →±∞ u  =  A  ≠ 0, or possesses compacton solutions only when lim x →±∞ u  = 0. Mathematical analysis and numerical simulations are provided for these soliton solutions of the K (2, 2) equation.

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