Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 33 min ago
PreprintarXiv licencearXiv

Scattering of group-invariant solutions below the ground state for the fourth-order NLS

  • Koichi Komada
Open at sourcePDFDOICite

Abstract

We consider the focusing, L2-supercritical and Ḣ2-subcritical nonlinear fourth-order Schrödinger equation. The scattering of radially symmetric solutions below the ground state was proved by Guo [Comm. Partial Differential Equations (2016)] and Dinh [Nonlinearity (2021)]. In this paper, we extend the scattering results to group-invariant solutions. In Komada--Masaki [Nonlinearity (2024)], the scattering of group-invariant solutions below the ground state was proved under a certain hypothesis. To remove the hypothesis, we establish the non-optimal scattering result for general solutions, where the threshold of action is less than certain fraction of the action of the ground state. This result is analogous to that in Pausader--Shao [J. Hyperbolic Differ. Equ. (2010)] for the L2-critical nonlinear fourth-order Schrödinger equation.

Related

  1. Scattering of non-radial solutions for the fourth-order Schrödinger equation with Ḣ1/2-critical and supercritical nonlinearity
    Takahisa Inui, Koichi Komada, Kuranosuke Nishimura
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. Solutions to fourth order degenerate parabolic equations obtained via weighted energy dissipation
    Daniel Matthes, Vera Pazukhina
    arXivPreprintarXiv licenceFull textAnalysis & PDEsGeometry & topologyarXiv
  3. Classification of Solutions to a Critical Fourth-Order Equation on Complete Non-compact Manifolds
    Huabin Li, Tian Wu, Xiao Zhou
    arXivPreprintarXiv licenceFull textAnalysis & PDEsGeometry & topologyarXiv
  4. The Fourth Continuous Bounded Cohomology of the Complex Symplectic Group
    Sixuan Gu, Yaoyu Cheng, Wei Qi
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Integral Representations for Solutions of the Linearized Fourth Painleve Equation
    Oleg M. Kiselev
    arXivPreprintarXiv licenceFull textGeometry & topologyMathematical physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{komada2026scattering,
  title = {{Scattering of group-invariant solutions below the ground state for the fourth-order NLS}},
  author = {Koichi Komada},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.33381},
  eprint = {2609.33381},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.33381},
}
RIS
TY  - UNPB
TI  - Scattering of group-invariant solutions below the ground state for the fourth-order NLS
AU  - Koichi Komada
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.33381
UR  - https://arxiv.org/abs/2609.33381
AB  - We consider the focusing, L^2-supercritical and Ḣ^2-subcritical nonlinear fourth-order Schrödinger equation. The scattering of radially symmetric solutions below the ground state was proved by Guo [Comm. Partial Differential Equations (2016)] and Dinh [Nonlinearity (2021)]. In this paper, we extend the scattering results to group-invariant solutions. In Komada--Masaki [Nonlinearity (2024)], the scattering of group-invariant solutions below the ground state was proved under a certain hypothesis. To remove the hypothesis, we establish the non-optimal scattering result for general solutions, where the threshold of action is less than certain fraction of the action of the ground state. This result is analogous to that in Pausader--Shao [J. Hyperbolic Differ. Equ. (2010)] for the L^2-critical nonlinear fourth-order Schrödinger equation.
ER  -