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TMF, 1974, Volume 19, Number 3, Pages 332–343 (Mi tmf3592)  

This article is cited in 15 scientific papers (total in 15 papers)

On the complete integrability of a nonlinear Schrödinger equation

V. E. Zakharov, S. V. Manakov


Abstract: It is shown that a nonlinear Schrödinger equation, regarded as the Hamiltonian of a system, is completely integrable. A transition to angle and action variables is made by means of the $S$-matrix of the one-dimensional Dirae operator.

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English version:
Theoretical and Mathematical Physics, 1974, 19:3, 551–559

Bibliographic databases:

Received: 16.04.1973

Citation: V. E. Zakharov, S. V. Manakov, “On the complete integrability of a nonlinear Schrödinger equation”, TMF, 19:3 (1974), 332–343; Theoret. and Math. Phys., 19:3 (1974), 551–559

Citation in format AMSBIB
\Bibitem{ZakMan74}
\by V.~E.~Zakharov, S.~V.~Manakov
\paper On the complete integrability of a~nonlinear Schr\"odinger equation
\jour TMF
\yr 1974
\vol 19
\issue 3
\pages 332--343
\mathnet{http://mi.mathnet.ru/tmf3592}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=468821}
\zmath{https://zbmath.org/?q=an:0293.35025}
\transl
\jour Theoret. and Math. Phys.
\yr 1974
\vol 19
\issue 3
\pages 551--559
\crossref{https://doi.org/10.1007/BF01035568}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. E. Korepin, L. D. Faddeev, “Quantization of solitons”, Theoret. and Math. Phys., 25:2 (1975), 1039–1049  mathnet  crossref  mathscinet
    2. I. Ya. Aref'eva, “Conservation laws for the four-fermion interaction in two-dimensional spacetime”, Theoret. and Math. Phys., 26:3 (1976), 205–207  mathnet  crossref  mathscinet
    3. V. E. Zakharov, S. V. Manakov, “Generalization of the inverse scattering problem method”, Theoret. and Math. Phys., 27:3 (1976), 485–487  mathnet  crossref  mathscinet  zmath
    4. P. P. Kulish, S. V. Manakov, L. D. Faddeev, “Comparison of the exact quantum and quasiclassical results for a nonlinear Schrödinger equation”, Theoret. and Math. Phys., 28:1 (1976), 615–620  mathnet  crossref  mathscinet  isi
    5. P. P. Kulish, “Factorization of the classical and the quantum $S$-matrix and conservation laws”, Theoret. and Math. Phys., 26:2 (1976), 132–137  mathnet  crossref  mathscinet
    6. B. A. Dubrovin, V. B. Matveev, S. P. Novikov, “Non-linear equations of Korteweg–de Vries type, finite-zone linear operators, and Abelian varieties”, Russian Math. Surveys, 31:1 (1976), 59–146  mathnet  crossref  mathscinet  zmath
    7. S. V. Manakov, “Example of a completely integrable nonlinear wave field with nontrivial dynamics (lee model)”, Theoret. and Math. Phys., 28:2 (1976), 709–714  mathnet  crossref  mathscinet  zmath
    8. V. P. Belavkin, V. P. Maslov, “Uniformization method in the theory of Nonlinear Hamiltonian systems of Vlasov and Hartree type”, Theoret. and Math. Phys., 33:1 (1977), 852–862  mathnet  crossref  mathscinet
    9. N. Yu. Reshetikhin, L. D. Faddeev, “Hamiltonian structures for integrable models of field theory”, Theoret. and Math. Phys., 56:3 (1983), 847–862  mathnet  crossref  mathscinet  isi
    10. I. M. Khamitov, “Local fields in the inverse scattering method”, Theoret. and Math. Phys., 62:3 (1985), 217–224  mathnet  crossref  mathscinet  isi
    11. V. D. Lipovskii, A. V. Shirokov, “$2+1$ Toda chain. II. Hamiltonian formalism”, Theoret. and Math. Phys., 84:1 (1990), 718–728  mathnet  crossref  mathscinet  isi
    12. S. V. Belyutin, “Investigation of the exact integrability of the multiwave Schrödinger equation”, Theoret. and Math. Phys., 110:2 (1997), 190–198  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. V. S. Gerdjikov, N. A. Kostov, T. I. Valchev, “Multicomponent nonlinear schrödinger equations with constant boundary conditions”, Theoret. and Math. Phys., 159:3 (2009), 787–795  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    14. Quantum Electron., 40:9 (2010), 756–781  mathnet  crossref  adsnasa  isi  elib
    15. Yakhshimuratov A., “The Nonlinear Schrodinger Equation with a Self-consistent Source in the Class of Periodic Functions”, Math Phys Anal Geom, 14:2 (2011), 153–169  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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