The periodic Korteweg–de Vries problem

In this paper we give a method for solving the periodic Cauchy problem for the Korteweg–de Vries equation:
\begin{gather*} v-6vv'+v'''=0,\qquad v(x,\,0)=v_0(x),\quad v(x+\pi,\,t)=v(x,\,t)\\ (-\infty<x<\infty,\quad-\infty<t<\infty). \end{gather*}

We justify our method with the aid of the theory of inverse spectral problems for Sturm–Liouville operators, considered on a finite interval.
Bibliography: 8 titles.