论文标题
分数korteweg-de vries类型方程的孤立波的衰减
Decay of solitary waves of fractional Korteweg-de Vries type equations
论文作者
论文摘要
我们研究了与$ 1 $二维半线性分数方程相关的分数korteweg-de vries类型方程的孤立波。 \ vert d \ vert^αu + u -f（u）= 0，\ end {align*}，带有$α\ in（0,2）$，一个规定的系数$ p^*（α）$和非线性$ f（u）$ f（u） $ f（u）= u^p $，带有整数$ p \ [2; p^*（α））$。就分散系数$α$和非线性$ P $而言，给出了无限解决方案的订单$ 1 $ $ 1 $的渐近开发以及阳性解决方案的二阶开发项目。主要工具是Bona和Li引入的内核配方，以及复杂分析理论对内核的准确描述。
We study the solitary waves of fractional Korteweg-de Vries type equations, that are related to the $1$-dimensional semi-linear fractional equations: \begin{align*} \vert D \vert^αu + u -f(u)=0, \end{align*} with $α\in (0,2)$, a prescribed coefficient $p^*(α)$, and a non-linearity $f(u)=\vert u \vert^{p-1}u$ for $p\in(1,p^*(α))$, or $f(u)=u^p$ with an integer $p\in[2;p^*(α))$. Asymptotic developments of order $1$ at infinity of solutions are given, as well as second order developments for positive solutions, in terms of the coefficient of dispersion $α$ and of the non-linearity $p$. The main tools are the kernel formulation introduced by Bona and Li, and an accurate description of the kernel by complex analysis theory.
