Solitary Waves in a Singularly Perturbed Camassa-Holm Equation Involving Atangana’s Conformable Derivative

• Zhenglong Zhang ^[1] ; Xiaowan Li ^[1]
  1. [1] Xinjiang University

     Xinjiang University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 2, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper establishes the existence of solitary wave solutions for a singularly perturbed Camassa-Holm equation with Atangana’s conformable derivative, where the singular perturbation is given by a Kuramoto-Sivashinsky (KS) term τ (Dx xv + Dxxxxv). Physically, the KS perturbation encodes small-scale dispersive effects due to viscosity and surface tension, while the conformable time derivative Dα t captures memory effects. The parameter k shifts the linear wave speed near the critical shallow-water velocity, and m = 2 corresponds to quadratic nonlinear advection. Using traveling wave coordinates, solitary waves are characterized as homoclinic orbits; by combining geometric singular perturbation, invariant manifold theory, and Fredholm orthogonality, this paper proves the existence of solitary waves under the KS perturbation. In this way, this result extends earlier existence theories by simultaneously accommodating the linear term 2k Dxv, quadratic nonlinearity m = 2, and the KS perturbation.

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