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Peakons and periodic cusp wave solutions in a generalized Camassa-Holm equation. (English) Zbl 1142.35591
Summary: By using the bifurcation theory of planar dynamical systems to a generalized Camassa-Holm equation $m_t+c_{0}u_x+um_x+2mu_x=-\gamma u_{xxx}$ with $m = u - \alpha ^{2}u_{xx}, \alpha \neq 0, c_{0}, \gamma $ 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.

35Q53KdV-like (Korteweg-de Vries) equations
35B10Periodic solutions of PDE
35C05Solutions of PDE in closed form
Full Text: DOI
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