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arXiv · 2111.15136

Orbital stability of two-component peakons

Cheng He·Xiaochuan Liu·Changzheng Qu
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Abstract

We prove that the two-component peakon solutions are orbitally stable in the energy space. The system concerned here is a two-component Novikov system, which is an integrable multicomponent extension of the integrable Novikov equation. We improve the method for the scalar peakons to the two-component case with genuine nonlinear interactions by establishing optimal inequalities for the conserved quantities involving the coupled structures. Moreover, we also establish the orbital stability for the train-profiles of these two-component peakons by using the refined analysis based on monotonicity of the local energy and an induction method.

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Cheng He, Xiaochuan Liu, Changzheng Qu. 2023-01-06. Orbital stability of two-component peakons. https://arxiv.org/abs/2111.15136

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