\begin{abstract} We show that if the initial profile $q\left( x\right) $ for the Korteweg-de Vries (KdV) equation is essentially semibounded from below and $\int^{\infty }x^{5/2}\left\vert q\left( x\right) \right\vert dx<\infty,$ (no decay at $-\infty$ is required) then the KdV has a unique global classical solution given by a determinant formula. This result is best known to date. \end{abstract}

中文翻译：

---

关于KdV方程的经典解

\ begin {abstract}我们表明，如果Korteweg-de Vries（KdV）方程的初始轮廓$ q \ left（x \ right）$本质上是从下方开始的，并且$ \ int ^ {\ infty} x ^ {5 / 2} \ left \ vert q \ left（x \ right）\ right \ vert dx <\ infty，$（不需要在$-\ infty $处进行衰减），则KdV具有行列式给出的唯一全局经典解公式。迄今为止，该结果最为人所知。\ end {摘要}