Exact loop solutions, cusp solutions, solitary wave solutions and periodic wave solutions for the special CH–DP equation

By using the method of dynamical systems, the travelling wave solutions of a special CH–DP equation are studied. Exact explicit parametric representations of smooth solitary waves, solitary cusp waves, breaking waves and uncountably infinitely many smooth periodic wave solutions are given. In different regions of the parametric plane, different phase portraits are determined. The so called loop soliton solution is discussed.