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Utilizing the methods of dynamical system theory, the DullinGottwald-Holm equation is studied in this paper. The dynamical behaviors of the traveling wave solutions and their bifurcations are presented in different parameter regions. Furthermore, the exact explicit forms of all possible bounded solutions, such as solitary wave solutions, periodic wave solutions and breaking loop wave solutions are obtained.

EXACT TRAVELING WAVE SOLUTIONS AND BIFURCATIONS FOR THE DULLIN-GOTTWALD-HOLM EQUATION