Geodesic
The periodic Korteweg--de~Vries problem
Sbornik. Mathematics, Tome 24 (1974) no. 3, pp. 319-344

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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\infty,\quad-\infty\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. 
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     author = {V. A. Marchenko},
     title = {The periodic {Korteweg--de~Vries} problem},
     journal = {Sbornik. Mathematics},
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     number = {3},
     year = {1974},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1974_24_3_a0/}
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V. A. Marchenko. The periodic Korteweg--de~Vries problem. Sbornik. Mathematics, Tome 24 (1974) no. 3, pp. 319-344. http://geodesic.mathdoc.fr/item/SM_1974_24_3_a0/