Orbital stability of solitary wave solutions of the derivative nonlinear Schrödinger equation in the endpoint case
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Shen, Jia, Wu, Yifei, Yang, Changping
Institution: Nankai University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221777869