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Single peak solitary wave solutions for the osmosis $$K(2,2)$$ equation under inhomogeneous boundary condition. (English) Zbl 1196.35180
Summary: The qualitative theory of differential equations is applied to the $$K$$(2,2) equation with osmosis dispersion. Smooth, peaked and cusped solitary wave solutions of the osmosis $$K$$(2,2) equation under inhomogeneous boundary condition are obtained. The parametric conditions of existence of the smooth, peaked and cusped solitary wave solutions are given by using the phase portrait analytical technique. Asymptotic analysis and numerical simulations are provided for smooth, peaked and cusped solitary wave solutions of the osmosis $$K$$(2,2) equation.

##### MSC:
 35Q53 KdV equations (Korteweg-de Vries equations) 35C08 Soliton solutions 35B65 Smoothness and regularity of solutions to PDEs 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 35B40 Asymptotic behavior of solutions to PDEs
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