中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人： 兰洋 （清华大学）
题 目：Strongly interacting multi-solitons for generalized Benjamin-Ono equations
时 间：2022.04.20（星期三）16:00-17:00
地 点：思源楼S713
摘 要：We consider the generalized Benjamin-Ono equation:
$$\partial_tu+\partial_x(-|D|u+|u|^{p-1}u)=0,$$ with $L^2$-supercritical power $p>3$ or $L^2$-subcritical power $2<p<3$. We will construct strongly interacting multi-solitary wave of the form: $\sum_{i=1}^nQ(\cdot-t-x_i(t))$, where $n\geq 2$, and the parameters $x_i(t)$ satisfying $x_{i}(t)-x_{i+1}(t)\sim \sqrt{t}$ as $t\rightarrow +\infty$. We will also prove the uniqueness of such solutions in the case of $n=2$ and $p>3$.
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