发表机构
Tsinghua University; Academy of Mathematics and Systems Science, Chinese Academy of Sciences（清华大学; 中国科学院数学与系统科学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明质量临界广义KdV方程存在具有对数相对距离和符号$(+,-,-)$的三孤子解，其存在性依赖于非线性相互作用生成的ODE系统的可解性，且动力学受强相互作用主导。
AI 中文摘要
对于质量临界广义Korteweg-de Vries方程，\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*} 我们证明了具有对数相对距离和符号选择$(+,-,-)$的三孤子解的存在性。数字三的选择和孤子的符号与由三个孤子之间的非线性相互作用以及某些非局部化轮廓所产生的常微分方程系统的可解性有关。特别地，这些特殊行为是由于三个孤子之间的强相互作用所致。也就是说，每个孤子的动力学在一阶上受到其他孤子存在的扰动。
英文摘要
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.
Comments46 pages
