A. N. Leznov, M. V. Saveliev, V. G. Smirnov, “Theory of group representations and integration of nonlinear dynamical systems”, TMF, 48:1 (1981), 3–12; Theoret. and Math. Phys., 48:1 (1981), 565

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Teoreticheskaya i Matematicheskaya Fizika, 1981, Volume 48, Number 1, Pages 3–12 (Mi tmf4466)

This article is cited in 25 scientific papers (total in 25 papers)

Theory of group representations and integration of nonlinear dynamical systems

A. N. Leznov, M. V. Saveliev, V. G. Smirnov

Full-text PDF (1102 kB) Citations (25)

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Abstract: For nonlinear two-dimensional dynamical systems associated with graded Lie algebras a method is developed for constructing general solutions. The construction is based on the realization of a Lax type representation by operators which take values in the corresponding algebra and uses the theory of representations of algebras.

Received: 11.04.1980

English version:
Theoretical and Mathematical Physics, 1981, Volume 48, Issue 1, Pages 565–571
DOI: https://doi.org/10.1007/BF01037979

Bibliographic databases:

Language: Russian

Citation: A. N. Leznov, M. V. Saveliev, V. G. Smirnov, “Theory of group representations and integration of nonlinear dynamical systems”, TMF, 48:1 (1981), 3–12; Theoret. and Math. Phys., 48:1 (1981), 565–571

Citation in format AMSBIB

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\jour Theoret. and Math. Phys.

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\pages 565--571

\crossref{https://doi.org/10.1007/BF01037979}

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Linking options:

https://www.mathnet.ru/eng/tmf4466

https://www.mathnet.ru/eng/tmf/v48/i1/p3

This publication is cited in the following 25 articles:

Katsushi Ito, Mingshuo Zhu, “WKB analysis of the linear problem for modified affine Toda field equations”, J. High Energ. Phys., 2023:8 (2023)
Jian Li, Chuanzhong Li, “Generalizations of the finite nonperiodic Toda lattice and its Darboux transformation”, Commun. Theor. Phys., 73:8 (2021), 085002
Dmitry Millionshchikov, “Lie Algebras of Slow Growth and Klein–Gordon PDE”, Algebr. Represent. Theory, 2018, 1–33
O. M. Kiselev, “Asymptotics of solutions of higher-dimensional integrable equations and their perturbations”, Journal of Mathematical Sciences, 138:6 (2006), 6067–6230
R Willox, I Loris, “An algebraic description of generalizedk-constraints”, J. Phys. A: Math. Gen., 32:10 (1999), 2027
A.N. Leznov, “Graded Lie algebras, representation theory, integrable mappings and systems. Non-abelian case”, Nuclear Physics B, 543:3 (1999), 652
J. J. C. Nimmo, R. Willox, “Darboux transformations for the two-dimensional Toda system”, Proc. R. Soc. Lond. A, 453:1967 (1997), 2497
J J C Nimmo, “Darboux transformations and the discrete KP equation”, J. Phys. A: Math. Gen., 30:24 (1997), 8693
Lecture Notes in Physics Monographs, 36, Self-Dual Chern-Simons Theories, 1995, 188
Guizhang Tu, Soliton Theory and Its Applications, 1995, 230
Marco A.C. Kneipp, David I. Olive, “Crossing and antisolitons in affine Toda theories”, Nuclear Physics B, 408:3 (1993), 565
Jean-Loup Gervais, Lochlainn O'Raifeartaigh, Alexander V. Razumov, Mikhail V. Saveliev, “Gauge conditions for the constrained-WZNW-Toda reductions”, Physics Letters B, 301:1 (1993), 41
David I. Olive, Mikhail V. Saveliev, Jonathan W.R. Underwood, “On a solitonic specialisation for the general solutions of some two-dimensional completely integrable systems”, Physics Letters B, 311:1-4 (1993), 117
V. V. Bazhanov, “Integrable quantum systems and classical Lie algebras”, Commun.Math. Phys., 113:3 (1987), 471
P. J. Vassiliou, “Coupled systems of nonlinear wave equations and finite-dimensional lie algebras II: A nonlinear system arising from the group G 6.1 and its exact integration”, Acta Appl Math, 8:2 (1987), 149
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
M. V. Saveliev, “Integrable supermanifolds and associated nonlinear equations”, Theoret. and Math. Phys., 59:3 (1984), 560–563
M. V. Saveliev, “Classification of exactly integrable embeddings of two-dimensional manifolds. The coefficients of the third fundamental forms”, Theoret. and Math. Phys., 60:1 (1984), 638–647
V. G. Drinfeld, V. V. Sokolov, “Lie algebras and equations of Korteweg–de Vries type”, J. Soviet Math., 30:2 (1985), 1975–2036
A. N. Leznov, M. V. Saveliev, “Nonlinear equations and graded Lie algebras”, J. Soviet Math., 36:6 (1987), 699–721

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

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References:	71
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