On classical solutions of the KdV equation

Abstract

\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 ${\int }^{\infty }{x}^{5/2}\left|q\left(x\right)\right|dx<\infty ,$ (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}