Existence and multiplicity of solutions for a coupled generalized Camassa-Holm system

Khaled Zennir; Svetlin G. Georgiev; Keltoum Bouhali; Amal Alhujaylan

doi:10.56947/amcs.v34.804

Authors

Khaled Zennir Department of Mathematics, College of Science, Qassim University, Saudi Arabia
Svetlin G. Georgiev Department of Mathematics, Sorbonne University, France
Keltoum Bouhali Department of Mathematics, College of Science, Qassim University, Saudi Arabia
Amal Alhujaylan Department of Mathematics, College of Science, Qassim University, Saudi Arabia

DOI:

https://doi.org/10.56947/amcs.v34.804

Keywords:

Nonlinear equations, generalized Camassa--Holm equations, coupled system, iterative methods, classical solutions.

Abstract

In this paper, we investigate the existence and multiplicity of solutions for a coupled system of generalized Camassa--Holm equations, which arise in the modeling of nonlinear wave propagation in dispersive media. By developing a new integral formulation of the problem and applying fixed-point techniques adapted to the coupled structure, we establish the existence of multiple physically relevant nonnegative classical solutions. In particular, we prove the existence of at least one, two, and three nonnegative solutions under suitable assumptions on the system parameters and initial data.