Peakons and periodic cusp wave solutions in a generalized Camassa–Holm equation |
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| Authors: | Lijun Zhang Li-Qun Chen Xuwen Huo |
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| Institution: | aSchool of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China;bShanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;cDepartment of Mechanics, Shanghai University, Shanghai 200444, China;dSchool of Information and Electronic, Zhejiang Sci-Tech University, Hangzhou 310018, China |
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| Abstract: | By using the bifurcation theory of planar dynamical systems to a generalized Camassa–Holm equation | with m = u − α2uxx, α ≠ 0, c0, γ are constant, which is called CH-r equation, the existence of peakons and periodic cusp wave solutions is obtained. The analytic expressions of the peakons and periodic cusp wave solutions are given and numerical simulation results show the consistence with the theoretical analysis at the same time.
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