Near-Ordinary Periodic Waves of a Generalized Reaction–Convection–Diffusion Equation

• Autores: Minzhi Wei, Xingwu Chen
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 3, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We investigate near-ordinary periodic traveling wave solutions bifurcated from a family of ordinary periodic traveling wave solutions for a generalized reaction– convection–diffusion equation, especially its dependence on the nonlinear reaction.

    Using the Abelian integral method and the Chebyshev criteria, we find conditions for the existence and number of near-ordinary periodic wave solutions not only for the monotone case of the ratio of the Abelian integral as previous publications, but also for the non-monotone case. In a parameter region we provide a conjecture about the uniqueness of near-ordinary periodic traveling wave solutions for any degree of the nonlinear reaction and prove it up to degree four. The final simulations illustrate theoretical results numerically

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