Some new soliton-like solutions and periodic wave solutions with loop or without loop to a generalized KdV equation

In this paper, by using the integral bifurcation method, we study a generalized KdV equation which was first derived by Fokas from physical considerations via a methodology of Fuchssteiner. All kinds of soliton-like or kink-like wave solutions and periodic wave solutions with loop or without loop are obtained. Smooth compacton-like periodic wave solution and non-smooth periodic cusp wave solution are also obtained. Their dynamic properties are investigated and their profiles are given by Mathematical software.