Strongly interacting multi-solitons for generalized Benjamin-Ono equations

Abstract

We consider the generalized Benjamin-Ono equation: $${\partial }_{t}u+{\partial }_x(-|D|u+|u{|}^{p-1}u)=0,$$ 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: ${\sum }_{i=1}^{n}Q(\cdot -t-x_i(t))$, where $n\ge 2$, and the parameters $x_i(t)$ satisfying $x_i(t)-x_{i+1}(t)\sim {\alpha }_k\sqrt{t}$ as $t\to +\infty$, for some universal positive constants ${\alpha }_k$. We will also prove the uniqueness of such solutions in the case of $n=2$ and $p>3$.

arXiv commentMore details are added, 63 pages