Geodesic
The periodic Korteweg–de Vries problem
Sbornik. Mathematics, Tome 24 (1974) no. 3, pp. 319-344 
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/
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     title = {The periodic {Korteweg{\textendash}de~Vries} problem},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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[5] V. A. Marchenko, “Periodicheskaya zadacha Kortevega-de Frisa”, DAN SSSR, 217:2 (1974), 276–279 | Zbl

[6] I. M. Gelfand, B. M. Levitan, “Ob opredelenii differentsialnogo uravneniya po ego spektralnoi funktsii”, Izv. AN SSSR, seriya matem., 15 (1951), 309–360 | MR | Zbl

[7] M. G. Gasymov, B. M. Levitan, “Opredelenie differentsialnogo operatora po dvum spektram”, Uspekhi matem. nauk, XIX:2 (116) (1964), 3–63 | MR

[8] S. P. Novikov, “Periodicheskaya zadacha dlya uravneniya Kortevega-de Frisa, I”, Funkts. analiz, 8:3 (1974), 54–66 | MR | Zbl