Periodic Waves and Monotonicity of Limit Wave Speed in a Perturbed Generalized KdV Equation with Two Arbitrarily High-Order Nonlinearities

• Xiuli Cen ^[1] ; Chunhang Zhang ^[1]
  1. [1] Central South University

     Central South University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 3, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper rigorously establishes the existence and number of periodic wave solutions for a perturbed generalized KdV (pgKdV) equation with two high-order nonlinearities (um)t + (um+)x + uxxx + ε(uxx + uxxxx ) = 0, where m and are arbitrary positive integers, and ε > 0 is a small parameter. By combining geometric singular perturbation theorywith the analysis of Abelian integral, we give the condition of wave speed for the existence and number of periodic wave solutions. Furthermore, the monotonicity of the limit wave speed is obtained by a classical and effective mathematical analysis method. Additionally, the upper and lower bounds of limit wave speed are derived. To our knowledge, this is the first complete result concerning the existence and number of periodic wave solutions for this class of pgKdV equation with arbitrary positive integers m and .

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