Geodesic
The inverse scattering method for a relativistic string
Teoretičeskaâ i matematičeskaâ fizika, Tome 57 (1983) no. 2, pp. 203-216 
G. P. Pron'ko. The inverse scattering method for a relativistic string. Teoretičeskaâ i matematičeskaâ fizika, Tome 57 (1983) no. 2, pp. 203-216. http://geodesic.mathdoc.fr/item/TMF_1983_57_2_a3/
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     author = {G. P. Pron'ko},
     title = {The inverse scattering method for a~relativistic string},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A relativistic string is described by the inverse scattering method for periodic potentials. The auxiliary spectral problem and the analytic properties of the Bloch functions are investigated. A complete set of involutive relativistieally invariant integrals of the motion is obtained. Equations are obtained for string configurations that have a finite number of gaps in the spectrum of the auxiliary problem. It is shown that such a condition is equivalent to stationarity of the configurations with respect to the higher string equations. The quantum theory in the single-gap sector is discussed.

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