Orbital stability of two-component peakons
Analysis of PDEs
2023-01-09 v2 Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.2111.15136,
title = {Orbital stability of two-component peakons},
author = {Cheng He and Xiaochuan Liu and Changzheng Qu},
journal= {arXiv preprint arXiv:2111.15136},
year = {2023}
}
Comments
Accepted for publication