Analytic and loop solutions for the K(2,2) equation (focusing branch)

In this paper, we study analytic and loop solutions of the K(2,2) equation(focusing branch), which is first proposed by Rosenau. The implicit analytic and loop solutions are obtained by using the dynamical system approach. Moreover, we investigate how the famous RosenauHyman compactons can be recovered as limits of classical solitary wave solutions forming analytic homoclinic orbits for the reduced dynamical system by theoretical analysis and numerical simulation.