Dynamics of Travelling Waves to KdV–Burgers–Kuramoto Equation with Marangoni Effect Perturbation

• Ke Wang ^[1] ; Shuting Chen ^[2] ; Zengji Du ^[1]
  1. [1] Jiangsu Normal University

     Jiangsu Normal University

     China

     
  2. [2] Southeast University

     Southeast University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 4, 2022
• Idioma: inglés
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• Resumen

  • This paper aims to establish the existence of travelling waves for a generalized KdV–Burgers–Kuramoto equation via utilising geometric singular perturbation theory. Firstly, we explore the existence results of orbits for the equation without delay and perturbation by employing Argument Principle. Secondly, the existence of travelling waves for the equation with two types of special delay convolution kernels are proved with the aid of combining the geometric singular perturbation theory, invariant manifold theory and Fredholm orthogonality theorem. Finally, asymptotic behaviors of traveling waves are given with the method of the asymptotic theory.