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Dokl. Akad. Nauk SSSR, 1974, Volume 219, Number 6, Pages 1334–1337 (Mi dan38752)  

This article is cited in 34 scientific papers (total in 35 papers)


Complete description of solutions of the “sine-Gordon” equation

V. E. Zakharov, L. A. Takhtadzhyan, L. D. Faddeev

Novosibirsk State University

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UDC: 517.946.4
Presented: . . 
Received: 06.12.1973

Citation: V. E. Zakharov, L. A. Takhtadzhyan, L. D. Faddeev, “Complete description of solutions of the “sine-Gordon” equation”, Dokl. Akad. Nauk SSSR, 219:6 (1974), 1334–1337

Citation in format AMSBIB
\by V.~E.~Zakharov, L.~A.~Takhtadzhyan, L.~D.~Faddeev
\paper Complete description of solutions of the ``sine-Gordon'' equation
\jour Dokl. Akad. Nauk SSSR
\yr 1974
\vol 219
\issue 6
\pages 1334--1337

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    This publication is cited in the following articles:
    1. A. K. Pogrebkov, V. N. Sushko, “Quantization of the $(\sin\varphi)_2$ interaction in terms of fermion variables”, Theoret. and Math. Phys., 24:3 (1975), 935–937  mathnet  crossref
    2. V. E. Korepin, L. D. Faddeev, “Quantization of solitons”, Theoret. and Math. Phys., 25:2 (1975), 1039–1049  mathnet  crossref  mathscinet
    3. 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
    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, E. R. Nisimov, “Anomalies of quantum currents in exactly solvable models”, Theoret. and Math. Phys., 29:2 (1976), 992–998  mathnet  crossref  mathscinet  zmath  isi
    6. V. A. Andreev, “Application of the inverse scattering method to the equation $\sigma_{xt}=e^\sigma$”, Theoret. and Math. Phys., 29:2 (1976), 1027–1032  mathnet  crossref  mathscinet
    7. 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
    8. 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
    9. A. V. Razumov, “Bogolyubov transformation and quantization of solitons”, Theoret. and Math. Phys., 30:1 (1977), 10–16  mathnet  crossref  mathscinet
    10. E. A. Kuznetsov, A. V. Mikhailov, “On the complete integrability of the two-dimensional classical Thirring model”, Theoret. and Math. Phys., 30:3 (1977), 193–200  mathnet  crossref  mathscinet
    11. I. M. Krichever, “Methods of algebraic geometry in the theory of non-linear equations”, Russian Math. Surveys, 32:6 (1977), 185–213  mathnet  crossref  mathscinet  zmath
    12. 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
    13. A. V. Zhiber, “Conservation laws for the equation $u_{tt}-u_{xx}+\sin u=0$”, Funct. Anal. Appl., 11:1 (1977), 55–57  mathnet  crossref  mathscinet  zmath
    14. V. N. Sushko, “Fermionization of the $(\sin\varphi)_2$ interaction in a box”, Theoret. and Math. Phys., 37:2 (1978), 949–969  mathnet  crossref  mathscinet
    15. V. E. Korepin, “Above-barrier reflection of solitons”, Theoret. and Math. Phys., 34:1 (1978), 1–8  mathnet  crossref
    16. I. V. Cherednik, “One generalization of the KdV and sin-Gordon differential equations”, Funct. Anal. Appl., 13:1 (1979), 68–69  mathnet  crossref  mathscinet  zmath
    17. E. K. Sklyanin, L. A. Takhtadzhyan, L. D. Faddeev, “Quantum inverse problem method. I”, Theoret. and Math. Phys., 40:2 (1979), 688–706  mathnet  crossref  mathscinet  isi
    18. A. K. Pogrebkov, “Complete integrability of dynamical systems generated by singular solutions of liouville's equation”, Theoret. and Math. Phys., 45:2 (1980), 951–957  mathnet  crossref  mathscinet  zmath  isi
    19. S. A. Vladimirov, “Automorphic systems of scalar fields”, Theoret. and Math. Phys., 46:1 (1981), 28–32  mathnet  crossref  mathscinet  zmath  isi
    20. A. K. Prikarpatskii, “Geometrical structure and Bäcklund transformations of nonlinear evolution equations possessing a Lax representation”, Theoret. and Math. Phys., 46:3 (1981), 249–256  mathnet  crossref  mathscinet  zmath  isi
    21. V. P. Maslov, G. A. Omel'yanov, “Asymptotic soliton-form solutions of equations with small dispersion”, Russian Math. Surveys, 36:3 (1981), 73–149  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    22. A. N. Leznov, “The inverse scattering method in a form invariant with respect to representations of the internal symmetry algebra”, Theoret. and Math. Phys., 58:1 (1984), 103–106  mathnet  crossref  mathscinet  isi
    23. A. N. Leznov, V. I. Man'ko, S. M. Chumakov, “Symmetries and soliton solutions of nonlinear equations”, Theoret. and Math. Phys., 63:1 (1985), 356–365  mathnet  crossref  mathscinet  zmath  isi
    24. A. N. Leznov, “Simplest soliton solutions of the equations of the periodic Toda chain of the series $A_k$ in the formalism of the scalar $L$$A$ pair”, Theoret. and Math. Phys., 71:3 (1987), 598–605  mathnet  crossref  mathscinet  isi
    25. Theoret. and Math. Phys., 92:3 (1992), 964–978  mathnet  crossref  mathscinet  zmath  isi
    26. Yu. S. Osipov, A. A. Gonchar, S. P. Novikov, V. I. Arnol'd, G. I. Marchuk, P. P. Kulish, V. S. Vladimirov, E. F. Mishchenko, “Lyudvig Dmitrievich Faddeev (on his sixtieth birthday)”, Russian Math. Surveys, 50:3 (1995), 643–659  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    27. G. A. Omel'yanov, D. A. Kulagin, “Asymptotics of Kink–Kink Interaction for Sine-Gordon Type Equations”, Math. Notes, 75:4 (2004), 563–567  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    28. A. B. Khasanov, G. U. Urazboev, “On the Sine–Gordon equation with a self-consistent source of the integral type”, Zhurn. matem. fiz., anal., geom., 2:3 (2006), 287–298  mathnet  mathscinet  zmath
    29. V. A. Andreev, “System of equations for stimulated combination scattering and the related double periodic $A_n^{(1)}$ Toda chains”, Theoret. and Math. Phys., 156:1 (2008), 1020–1027  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    30. A. B. Khasanov, G. U. Urazboev, “Integration of the sine-Gordon equation with a self-consistent source of the integral type in the case of multiple eigenvalues”, Russian Math. (Iz. VUZ), 53:3 (2009), 45–55  mathnet  crossref  mathscinet  zmath
    31. L. A. Takhtajan, A. Yu. Alekseev, I. Ya. Aref'eva, M. A. Semenov-Tian-Shansky, E. K. Sklyanin, F. A. Smirnov, S. L. Shatashvili, “Scientific heritage of L. D. Faddeev. Survey of papers”, Russian Math. Surveys, 72:6 (2017), 977–1081  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    32. Thomas Kappeler, Yannick Widmer, “On spectral properties of the $L$ operator in the Lax pair of the sine-Gordon equation”, Zhurn. matem. fiz., anal., geom., 14:4 (2018), 452–509  mathnet  crossref
    33. A. B. Hasanov, M. M. Hasanov, “Integration of the nonlinear Schrödinger equation with an additional term in the class of periodic functions”, Theoret. and Math. Phys., 199:1 (2019), 525–532  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    34. A. B. Khasanov, M. M. Matjakubov, “Integration of the nonlinear Korteweg–de Vries equation with an additional term”, Theoret. and Math. Phys., 203:2 (2020), 596–607  mathnet  crossref  crossref  mathscinet  isi  elib
    35. K. A. Mamedov, “Integration of mKdV equation with a self-consistent source in the class of finite density functions in the case of moving eigenvalues”, Russian Math. (Iz. VUZ), 64:10 (2020), 66–78  mathnet  crossref  crossref  isi
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