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Exact traveling wave solutions and bifurcations for the Dullin-Gottwald-Holm equation |
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| Authors: | Weiqin Yu Na Li Fangqi Chen and Shouwei Zhao |
| Institution: | School of Fundamental Studies, Shanghai University of Engineering Science, Longteng street, 201620, Shanghai, China,School of Fundamental Studies, Shanghai University of Engineering Science, Longteng street, 201620, Shanghai, China,Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Yudao street, 210016, Nanjing, China and School of Fundamental Studies, Shanghai University of Engineering Science, Longteng street, 201620, Shanghai, China |
| Abstract: | Utilizing the methods of dynamical system theory, the Dullin-Gottwald-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. |
| Keywords: | Dullin-Gottwald-Holm equation bifurcation solitary wave solution periodic wave solution breaking loop wave solution |
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