论文标题
分数修改的korteweg-de vries方程的强烈相互作用的孤立波
Strongly interacting solitary waves for the fractional modified Korteweg-de Vries equation
论文作者
论文摘要
我们研究了分数修改的korteweg-de vries方程的解决方案的一种特定渐近行为（也称为分散概括的修改后的benjamin-ono方程）：\ beken {align} \ tag {fmkdv} \ partial_t u + \ partial_x（ - \ vert d \ vert^αu + u^3）= 0。 \ end {align}偶极溶液是一种在很大程度上表现的解决方案，作为两个具有不同符号的强烈相互作用的孤立波的总和。我们证明了FMKDV的偶极子的存在。本文的新颖性是精确概况的构造。此外，要处理非本地运算符$ \ vert d \ vert^α$，我们会完善一些加权换向器的估计。
We study one particular asymptotic behaviour of a solution of the fractional modified Korteweg-de Vries equation (also known as the dispersion generalised modified Benjamin-Ono equation): \begin{align}\tag{fmKdV} \partial_t u + \partial_x (-\vert D \vert^αu + u^3)=0. \end{align} The dipole solution is a solution behaving in large time as a sum of two strongly interacting solitary waves with different signs. We prove the existence of a dipole for fmKdV. A novelty of this article is the construction of accurate profiles. Moreover, to deal with the non-local operator $\vert D \vert^α$, we refine some weighted commutator estimates.
