Skip to content
DraconiticResearch
Search Sources API
203,948 studies31 sourcesUpdated 40 min ago
PreprintarXiv licencearXiv

Stability in the log-modified nonlinear Schrödinger equation in dimension one

  • Daniele Garrisi
  • Yihan Liang
Open at sourcePDFDOICite

Abstract

In the one-dimensional log-modified nonlinear Schrödinger equation, there are finitely many normalised standing-waves, up to space translation and phase multiplication. In the defocusing case, there is exactly one normalised standing-wave having a prescribed mass and least energy. Both results are obtained by exploiting properties of the mass function: the analyticity in the focusing case, and the monotonicity in the defocusing case.

Related

  1. Large-data modified wave operators for the defocusing nonlinear Schrödinger equation in one space dimension with subcritical long-range nonlinearity
    Masaki Kawamoto, Haruya Mizutani
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  2. Stability of Solitons in the Parametrically Driven and Damped Nonlinear Schrödinger Equation in Arbitrary Dimension
    Fernando Carreño-Navas
    arXivPreprintarXiv licenceFull textMathematical physicsStatistical & nonlinear physicsarXiv
  3. Orbital stability of solitary wave solutions of the derivative nonlinear Schrödinger equation in the endpoint case
    Jia Shen, Yifei Wu, Changping Yang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Nonlinear coercivity and orbital stability of smooth solitary waves for the modified Camassa--Holm equation
    Xijun Deng, Ji Li, Zhisu Liu
    arXivPreprintCC BY-NC-SA 4.0Full textAnalysis & PDEsarXiv
  5. Global well-posedness for the derivative nonlinear Schrödinger equation on the circle
    Hajer Bahouri, Galina Perelman
    HALPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsHALarXiv

Cite

BibTeXRIS
BibTeX
@misc{garrisi2026stability,
  title = {{Stability in the log-modified nonlinear Schrödinger equation in dimension one}},
  author = {Daniele Garrisi and Yihan Liang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13833},
  eprint = {2609.13833},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13833},
}
RIS
TY  - UNPB
TI  - Stability in the log-modified nonlinear Schrödinger equation in dimension one
AU  - Daniele Garrisi
AU  - Yihan Liang
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.13833
UR  - https://arxiv.org/abs/2609.13833
AB  - In the one-dimensional log-modified nonlinear Schrödinger equation, there are finitely many normalised standing-waves, up to space translation and phase multiplication. In the defocusing case, there is exactly one normalised standing-wave having a prescribed mass and least energy. Both results are obtained by exploiting properties of the mass function: the analyticity in the focusing case, and the monotonicity in the defocusing case.
ER  -