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Existence of periodic waves for a perturbed quintic BBM equation

  • * Corresponding author: Yulin Zhao

    * Corresponding author: Yulin Zhao

This research is supported by the NSF of China (No.11971495 and No.11801582)

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  • This paper dealt with the existence of periodic waves for a perturbed quintic BBM equation by using geometric singular perturbation theory. By analyzing the perturbations of the Hamiltonian vector field with a hyperelliptic Hamiltonian of degree six, we proved that periodic wave solutions persist for sufficiently small perturbation parameter. It is also proved that the wave speed $ c_0(h) $ is decreasing on $ h $ by analyzing the ratio of Abelian integrals, where $ h $ is the energy level value. Moreover, the upper and lower bounds of the limit wave speed are given.

    Mathematics Subject Classification: Primary: 34C25, 34C60; Secondary: 37C27.


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  • Figure 1.  The phase portrait of system (1.13)

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