Construction of three-solitons with logarithmic distance for the mass-critical gKdV equations
Year: 2026
Type: preprint
Abstract: For the mass-critical generalized Korteweg-de Vries equation, \begin{equation*} \partial_{t}u+\partial_{x}\left( \partial_{x}^{2}u+u^{5}\right)=0,\quad (t,x)\in [0,\infty)\times \mathbb{R}, \end{equation*} 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.
Source: arXiv (Cornell University)
Authors: Lan, Yang, Yuan, Xu
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7211985748