New exact solutions for mCH and mDP equations by auxiliary equation method

With the aid of symbolic computation, auxiliary equation method is introduced to investigate modified forms of Camassa–Holm and Degasperis–Procesi equations. A series of new exact traveling wave solutions, including smooth solitary wave solution, peakons, singular solution, periodic wave solution, Jacobi elliptic solution, are obtained in general form. These new exact solutions will enrich previous results and help us further understand the physical structures of these two nonlinear equations.