Orbital stability of two-component peakons

TL;DR

This paper proves the orbital stability of two-component peakon solutions in a coupled Novikov system, extending scalar peakon stability methods to multicomponent integrable systems with nonlinear interactions.

Contribution

It introduces a novel approach to establish orbital stability for two-component peakons, including train-profiles, using optimal inequalities and refined monotonicity analysis.

Findings

Two-component peakons are orbitally stable in the energy space.

Stability of train-profiles of two-component peakons is also established.

The method extends scalar peakon stability techniques to multicomponent 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.