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PreprintCC BY 4.0HAL

Existence of multi-solitons for logarithmic Schrödinger equation with a perturbation of a smooth L2-subcritical function nonlinearity

  • Mohamed Bensaid
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Abstract

In this paper, we study the nonlinear Schrödinger equation with a nonlinearity combining a focusing logarithmic term and a smooth L2-subcritical function. Our main result is the construction of multisoliton solutions for this equation. These special configurations behave asymptotically, for large times, as the superposition of several solitons moving with distinct velocities. The proof relies on an iterative construction method combined with localized energy estimates adapted to the mixed structure of the nonlinearity.

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Cite

BibTeXRIS
BibTeX
@misc{bensaid2026existence,
  title = {{Existence of multi-solitons for logarithmic Schrödinger equation with a perturbation of a smooth $L^2$-subcritical function nonlinearity}},
  author = {Mohamed Bensaid},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18625},
  eprint = {2609.18625},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05749149v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Existence of multi-solitons for logarithmic Schrödinger equation with a perturbation of a smooth L^2-subcritical function nonlinearity
AU  - Mohamed Bensaid
PY  - 2026
DA  - 2026/09/14
PB  - HAL
DO  - 10.48550/arxiv.2609.18625
UR  - https://hal.science/hal-05749149v1
AB  - In this paper, we study the nonlinear Schrödinger equation with a nonlinearity combining a focusing logarithmic term and a smooth L^2-subcritical function. Our main result is the construction of multisoliton solutions for this equation. These special configurations behave asymptotically, for large times, as the superposition of several solitons moving with distinct velocities. The proof relies on an iterative construction method combined with localized energy estimates adapted to the mixed structure of the nonlinearity.
ER  -