Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 1 h ago
PreprintarXiv licencearXiv

The virial--Kato method and the asymptotic stability of solitons of the generalized Benjamin, Bona and Mahony equation

  • Scipio Cuccagna
  • Daniele Del Santo
  • Masaya Maeda
Open at sourcePDFDOICite

Abstract

We apply to the generalized pure power Benjamin, Bona and Mahony equation our method of combining high energy virial estimates with Kato smoothing, which closes the virial estimates in a natural way and allows us to prove a result of asymptotic stability for all the stable solitons with c>1 for all the exponents p>1.

Related

  1. The asymptotic stability of the stable solitons of the generalized good Boussinesq equation
    Junsik Bae, Scipio Cuccagna, Daniele Del Santo +1
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. Asymptotic Stability of Multi-Solitons for Coupled Nonlinear Schrödinger Equations via the ∂̅-Method
    Yubin Huang, Liming Ling, Huajie Su
    arXivPreprintarXiv licenceFull textAnalysis & PDEsMathematical physicsarXiv
  3. Spectral stability of resonant Y-solitons for the KP-II equation
    Tetsu Mizumachi
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Stability of Solitons in the Parametrically Driven and Damped Nonlinear Schrödinger Equation in Arbitrary Dimension
    Fernando Carreño-Navas
    arXivPreprintarXiv licenceFull textMathematical physicsStatistical & nonlinear physicsarXiv
  5. Asymptotic stability of Bloch wall for dispersive Landau-Lifshitz equation
    Slim Ibrahim, Christof Melcher, Ikkei Shimizu
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{cuccagna2026virialkato,
  title = {{The virial--Kato method and the asymptotic stability of solitons of the generalized Benjamin, Bona and Mahony equation}},
  author = {Scipio Cuccagna and Daniele Del Santo and Masaya Maeda},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41549},
  eprint = {2610.41549},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41549},
}
RIS
TY  - UNPB
TI  - The virial--Kato method and the asymptotic stability of solitons of the generalized Benjamin, Bona and Mahony equation
AU  - Scipio Cuccagna
AU  - Daniele Del Santo
AU  - Masaya Maeda
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41549
UR  - https://arxiv.org/abs/2610.41549
AB  - We apply to the generalized pure power Benjamin, Bona and Mahony equation our method of combining high energy virial estimates with Kato smoothing, which closes the virial estimates in a natural way and allows us to prove a result of asymptotic stability for all the stable solitons with c>1 for all the exponents p>1.
ER  -