Single peak solitary wave solutions for the osmosis equation under inhomogeneous boundary condition

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.