  In this paper, by using bifurcation method, we successfully find the
K(2,2)equation with osmosis dispersion possess two new types of travelling wave
solu tions 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.
