A three-component Camassa-Holm system with cubic nonlinearity and peakons
Baoqiang Xia, Ruguang Zhou, Zhijun Qiao
TL;DR
This paper introduces a new three-component Camassa-Holm system with cubic nonlinearity, demonstrating its integrability and peakon solutions, and explores related reduced equations with similar properties.
Contribution
It presents a novel integrable 3CH system with cubic nonlinearity, including its Lax pair, Hamiltonian structure, and peakon solutions, expanding the class of integrable peakon equations.
Findings
The 3CH system is integrable with a Lax pair, Hamiltonian structure, and conservation laws.
The system admits peakon and multi-peakon solutions.
Reductions lead to a new integrable perturbed CH equation with peakons.
Abstract
In this paper, we propose a three-component Camassa-Holm (3CH) system with cubic nonlinearity and peakons. The 3CH model is proven integrable in the sense of Lax pair, Hamiltonian structure, and conservation laws. We show that this system admits peaked soliton (peakon) and multi-peakon solutions. Additionally, reductions of the 3CH system are investigated so that a new integrable perturbed CH equation with cubic nonlinearity is generated to possess peakon solutions.
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Taxonomy
TopicsNonlinear Waves and Solitons · Nonlinear Photonic Systems · Algebraic structures and combinatorial models