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PreprintCC0arXiv

Construction of three-solitons with logarithmic distance for the mass-critical gKdV equations

  • Yang Lan
  • Xu Yuan
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Abstract

For the mass-critical generalized Korteweg-de Vries equation, ∂tu+∂x( ∂x2u+u5)=0, (t,x)∈ [0,∞)× ℝ, we prove the existence of three-soliton solutions with logarithmic relative distance and with the choice of signs (+,−,−). The choice of the number three and the signs of solitons are related to the solvability of the ODE system generated by the nonlinear interactions between the three solitons and some non-localized profiles. In particular, these special behaviors are due to strong interactions between the three solitons. That is, the dynamics of each soliton is perturbed at leading order by the presence of other solitons.

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Cite

BibTeXRIS
BibTeX
@misc{lan2026construction,
  title = {{Construction of three-solitons with logarithmic distance for the mass-critical gKdV equations}},
  author = {Yang Lan and Xu Yuan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08085},
  eprint = {2609.08085},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08085},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Construction of three-solitons with logarithmic distance for the mass-critical gKdV equations
AU  - Yang Lan
AU  - Xu Yuan
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08085
UR  - https://arxiv.org/abs/2609.08085
AB  - For the mass-critical generalized Korteweg-de Vries equation, ∂_tu+∂_x( ∂_x^2u+u^5)=0, (t,x)∈ [0,∞)× ℝ, we prove the existence of three-soliton solutions with logarithmic relative distance and with the choice of signs (+,−,−). The choice of the number three and the signs of solitons are related to the solvability of the ODE system generated by the nonlinear interactions between the three solitons and some non-localized profiles. In particular, these special behaviors are due to strong interactions between the three solitons. That is, the dynamics of each soliton is perturbed at leading order by the presence of other solitons.
ER  -