Solitary Wave, Periodic Cusp Wave and Compactons of the (2+1)-Dimensional KP-Like K(m,n) Equation

By using the bifurcation theory of dynamical systems to the generalized KP equation, under different parametric conditions, various sufficient conditions to guarantee the existence of the solitary wave solutions, periodic cusp wave solutions and compactons solutions are given. Some exact explicit parametric representations of the above waves are determined.