Geodesic
Backlund transformation for the nonlinear Schrodinger equation
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 27, Tome 494 (2020), pp. 5-22 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the note we give a new method of derivation of the Backlund transformation for the nonlinear Schrodinger equation. We discuss conserved quantities related to this transformation, and how it can be connected with the inverse scattering method. Besides, we construct a quantum analog of the Backlund transformation defined by the Baxter's $Q$-operator. 
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     author = {N. M. Belousov},
     title = {Backlund transformation for the nonlinear {Schrodinger} equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     year = {2020},
     volume = {494},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_494_a0/}
}
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N. M. Belousov. Backlund transformation for the nonlinear Schrodinger equation. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 27, Tome 494 (2020), pp. 5-22. http://geodesic.mathdoc.fr/item/ZNSL_2020_494_a0/

[1] B. G. Konopelchenko, “The group structure of Backlund transformations”, Phys. Lett. A, 74 (1979), 189–192 | DOI | MR

[2] R. Sasaki, “Canonical structure of Backlund transformations”, Phys. Lett. A, 78 (1980), 7–10 | DOI | MR

[3] B. G. Konopelchenko, “Elementary Backlund transformations, nonlinear superposition principle and solution of the integrable equations”, Phys. Lett. A, 87 (1982), 445–448 | DOI | MR

[4] V. B. Kuznetsov, E. K. Sklyanin, “On Backlund transformations for many-body systems”, J. Physics A, 31 (1998), 2241–2251, arXiv: solv-int/9711010 | DOI | MR | Zbl

[5] E. K. Sklyanin, “Backlund transformations and Baxter's Q-operator”, Integrable systems: from classical to quantum, Lecture notes (Universite de Montreal, Jul 26 – Aug 6 1999), arXiv: nlin/0009009 [nlin.SI] | MR

[6] A. G. Izergin, Introduction to the Bethe Ansatz Solvable Models, Lecture notes, Universit`a di Firenze, Dipartimento di Fisica, 1998–1999

[7] V. Fock, “On the canonical transformation in classical and quantum mechanics”, Acta Physica, 27 (1969), 219–224 | DOI | MR

[8] N. Belousov, S. Derkachov, “The $Q$-Operator for the Quantum NLS Model”, J. Math. Sci., 242 (2019), 608–627, arXiv: 1812.10043 [hep-th] | DOI | MR | Zbl

[9] E. K. Sklyanin, “Kvantovyi variant metoda obratnoi zadachi rasseyaniya”, Zap. nauchn. semin. LOMI, 95, 1980, 55–128 | Zbl

[10] F. A. Berezin, The method of second quantization, Pure Appl. Phys., 24, Academic Press, 1966, 228 pp. | MR | Zbl

[11] M. Gaudin, V. Pasquier, “The periodic Toda chain and a matrix generalization of the Bessel function's recursion relations”, J. Phys. A, 25 (1992), 5243–5252 | DOI | MR | Zbl