Existence of Kink Waves and Periodic Waves for a Perturbed Defocusing mKdV Equation

• Chen, Aiyong ^[1] ; Guo, Lina ^[1] ; Huang, Wentao ^[2]
  1. [1] Guilin University of Electronic Technology

     Guilin University of Electronic Technology

     China

     
  2. [2] Guilin University of Aerospace Technology

     Guilin University of Aerospace Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 17, Nº 3, 2018, págs. 495-517
• Idioma: inglés
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• Resumen

  • The existence of kink waves and periodic waves for a perturbed defocusing mKdV equation is established by using geometric singular perturbation theory. In addition, by analyzing the perturbation of the Hamiltonian vector field with an elliptic Hamiltonian of degree four, a two saddle cycle is exhibited. It is proven that the wave speed c0(h) is decreasing on h∈[-3/4,0] by analyzing the ratio of Abelian integrals and the limit of wave speed is given. Furthermore, the relationship between the wave speed and the wavelength of traveling waves is obtained.