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arXiv · 2610.15507

Orbital stability of solitary wave solutions of the derivative nonlinear Schrödinger equation in the endpoint case

Jia Shen·Yifei Wu·Changping Yang
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Abstract

In this paper, we consider the orbital stability of solitary waves for the derivative nonlinear Schrödinger equation $$iq_t+q_{xx}+i\partial_x\bigl(|q|^2q\bigr)=0, \quad (t,x)\in\mathbb{R}\times\mathbb{R}.$$ For the endpoint solitary waves satisfying $c>0$ and $c^2=4ω$, we prove the orbital stability in $H^1(\mathbb{R})$ without any additional assumptions. The proof uses conservation of mass and the second Hamiltonian $\mathcal{H}_2$ to keep the Bäcklund-transformed solution small in $H^1(\mathbb{R})$ uniformly in time. We establish an inverse Bäcklund compactness result to reconstruct the algebraic solitary wave as the spectral zero approaches the negative real axis.

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Jia Shen, Yifei Wu, Changping Yang. 2026-10-11. Orbital stability of solitary wave solutions of the derivative nonlinear Schrödinger equation in the endpoint case. https://arxiv.org/abs/2610.15507

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