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TMF, 1982, Volume 53, Number 2, Pages 227–237 (Mi tmf4377)  

This article is cited in 13 scientific papers (total in 13 papers)

Darboux transformations for non-Abelian and nonlocal equations of the Toda chain type

M. A. Sall'


Abstract: Darboux transformations are used to construct explicit solutions for the two-dimensionalized Toda chain, sine-Gordon equations and their non-Abelian analogs, the nonlinear Schrödinger equation, the nonlocal Toda equation, and non-Abelian equations of Langmuir oscillations.

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English version:
Theoretical and Mathematical Physics, 1982, 53:2, 1092–1099

Bibliographic databases:

Received: 25.12.1981

Citation: M. A. Sall', “Darboux transformations for non-Abelian and nonlocal equations of the Toda chain type”, TMF, 53:2 (1982), 227–237; Theoret. and Math. Phys., 53:2 (1982), 1092–1099

Citation in format AMSBIB
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\by M.~A.~Sall'
\paper Darboux transformations for non-Abelian and nonlocal equations of the Toda chain type
\jour TMF
\yr 1982
\vol 53
\issue 2
\pages 227--237
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\zmath{https://zbmath.org/?q=an:0523.35095}
\transl
\jour Theoret. and Math. Phys.
\yr 1982
\vol 53
\issue 2
\pages 1092--1099
\crossref{https://doi.org/10.1007/BF01016678}
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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. A. V. Rybin, M. A. Sall', “Solitons of the Korteweg-de Vries equation on the background of a known solution”, Theoret. and Math. Phys., 63:3 (1985), 545–550  mathnet  crossref  mathscinet  zmath  isi
    2. N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, “Exact first-order solutions of the nonlinear Schrödinger equation”, Theoret. and Math. Phys., 72:2 (1987), 809–818  mathnet  crossref  mathscinet  zmath  isi
    3. A. R. Its, A. V. Rybin, M. A. Sall', “Exact integration of nonlinear Schrödinger equation”, Theoret. and Math. Phys., 74:1 (1988), 20–32  mathnet  crossref  mathscinet  zmath  isi
    4. V. D. Lipovskii, A. V. Shirokov, “$2+1$ Toda chain. I. Inverse scattering method”, Theoret. and Math. Phys., 75:3 (1988), 555–566  mathnet  crossref  mathscinet  isi
    5. O. I. Bogoyavlenskii, “Algebraic constructions of integrable dynamical systems-extensions of the Volterra system”, Russian Math. Surveys, 46:3 (1991), 1–64  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. S. B. Leble, “Necessary Covariance Conditions for a One-Field Lax Pair”, Theoret. and Math. Phys., 144:1 (2005), 985–994  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Leble S., “Covariant forms of Lax one-field operators: From abelian to noncommutative”, Bilinear Integrable Systems: From Classical to Quatum, Continuous to Discrete, Nato Science Series, Series II: Mathematics, Physics and Chemistry, 201, 2006, 161–173  isi
    8. Adler, VE, “On vector analogs of the modified Volterra lattice”, Journal of Physics A-Mathematical and Theoretical, 41:45 (2008), 455203  crossref  mathscinet  zmath  adsnasa  isi
    9. Li, CX, “Quasideterminant solutions of a non-Abelian Toda lattice and kink solutions of a matrix sine-Gordon equation”, Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 464:2092 (2008), 951  crossref  isi
    10. E. O. Pozdeeva, “A new two-parameter family of exactly solvable Dirac Hamiltonians”, Theoret. and Math. Phys., 159:2 (2009), 618–626  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    11. Dubard P., Matveev V.B., “Multi-Rogue Waves Solutions: From the NLS to the KP-I Equation”, Nonlinearity, 26:12 (2013), R93–R125  crossref  isi
    12. V. B. Matveev, F. Dyubard, A. O. Smirnov, “Kvaziratsionalnye resheniya nelineinogo uravneniya Shrëdingera”, Nelineinaya dinam., 11:2 (2015), 219–240  mathnet
    13. Ariznabarreta G. Garcia-Ardila J.C. Manas M. Marcellan F., “Non-Abelian Integrable Hierarchies: Matrix Biorthogonal Polynomials and Perturbations”, J. Phys. A-Math. Theor., 51:20 (2018), 205204  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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