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

@misc{shen2026orbital,
  title = {{Orbital stability of solitary wave solutions of the derivative nonlinear Schrödinger equation in the endpoint case}},
  author = {Jia Shen and Yifei Wu and Changping Yang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15507},
  eprint = {2610.15507},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15507},
}

TY  - UNPB
TI  - Orbital stability of solitary wave solutions of the derivative nonlinear Schrödinger equation in the endpoint case
AU  - Jia Shen
AU  - Yifei Wu
AU  - Changping Yang
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15507
UR  - https://arxiv.org/abs/2610.15507
AB  - In this paper, we consider the orbital stability of solitary waves for the derivative nonlinear Schrödinger equation iq_t+q_xx+i∂_x(|q|^2q)=0, (t,x)∈ℝ×ℝ. For the endpoint solitary waves satisfying c>0 and c^2=4ω, we prove the orbital stability in H^1(ℝ) without any additional assumptions. The proof uses conservation of mass and the second Hamiltonian ℋ_2 to keep the Bäcklund-transformed solution small in H^1(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.
ER  -