Geodesic
Derivation of the Bäcklund transformation in the formalism of the inverse scattering problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 39 (1979) no. 1, pp. 69-74 
V. S. Gerdjikov; P. P. Kulish. Derivation of the Bäcklund transformation in the formalism of the inverse scattering problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 39 (1979) no. 1, pp. 69-74. http://geodesic.mathdoc.fr/item/TMF_1979_39_1_a6/
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     title = {Derivation of the {B\"acklund} transformation in the formalism of the inverse scattering problem},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The formal solution of the Gel'fand–Levitan–Marchenko equation is used to obtain the Bäcklund transformation for the class of nonlinear evolution equations that are solvable by the formalism of the inverse scattering problem for the Dirac operator with constant boundary conditions.

[1] L. P. Eisenhart, A Treatise on the Differential Geometry of Curves and Surfaces, Dover Publ., N. Y., 1960 | MR

[2] F. Calogero, A. Degasperis, Nuovo Cim., 32B (1974), 201 | MR

[3] G. L. Lamb. Jr., J. Math. Phys., 15 (1974), 2157 | DOI | MR

[4] H. H. Chen, Phys. Rev. Lett., 33 (1974), 925 | DOI | MR | Zbl

[5] M. Wadati, H. Sanuki, K. Konno, Progr. Theor. Phys., 53 (1975), 419 | DOI | MR | Zbl

[6] V. S. Gerdzhikov, P. P. Kulish, Volg. fiz. zh., 5 (1978), 337 | MR

[7] P. P. Kulish, S. V. Manakov, L. D. Faddeev, TMF, 28 (1976), 38 | MR

[8] L. D. Faddeev, UMN, 14 (1959), 57 | MR

[9] R. Jost, W. Kohn, Kgl. Danske Videnskab. Selbkab, Mat. fys. Medd., 27 (1953), 9 ; R. Newton, J. Math. Phys., 1 (1960), 319 | MR | Zbl | DOI | MR | Zbl

[10] R. K. Dodd, R. K. Bullough, Phys. Lett., 62A (1977), 70 | DOI | MR