论文标题
用于广义的本杰明·索方程的强烈相互作用的多soliton
Strongly interacting multi-solitons for generalized Benjamin-Ono equations
论文作者
论文摘要
我们考虑广义的Benjamin-ono方程：$$ \ partial_tu+\ partial_x（ - | d | d | u+| u | u |^{p-1} u |^{p-1} u）= 0，$ l^2 $ l^2 $ -supercrical Power $ p> 3 $ p> 3 $或$ l^2 $ l^2 $ -subcritical power $ 2 $ 2 <p <p <p <p <3 $。我们将构建形式的强烈交互的多单位波：$ \ sum_ {i = 1}^nq（\ cdot-t-x_i（t））$，其中$ n \ geq 2 $和参数$ x_i（t）$满足$ x_i（t）$满足$ x__ {i}（t）（t） - x_（t）-x_ {i+1} $+sim+sim+1} $ t \ rightarrow +\ infty $，对于某些通用正常数$α_k$。在$ n = 2 $和$ p> 3 $的情况下，我们还将证明此类解决方案的独特性。
We consider the generalized Benjamin-Ono equation: $$\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 $x_{i}(t)-x_{i+1}(t)\sim α_k \sqrt{t}$ as $t\rightarrow +\infty$, for some universal positive constants $α_k$. We will also prove the uniqueness of such solutions in the case of $n=2$ and $p>3$.
