New exact travelling wave solutions for the K(2, 2) equation with osmosis dispersion

In this paper, by using bifurcation method, we successfully find the K(2, 2) equation with osmosis dispersion ut+(u )x− (u)xxx = 0 possess two new types of travelling wave solutions called kink-like wave solutions and antikink-like wave solutions. They are defined on some semifinal bounded domains and possess properties of kink waves and anti-kink waves. Their implicit expressions are obtained. For some concrete data, the graphs of the implicit functions are displayed, and the numerical simulation of travelling wave system is made by Maple. The results show that our theoretical analysis agrees with the numerical simulation.