V. E. Adler, V. G. Marikhin, A. B. Shabat, “Lagrangian Chains and Canonical Bäcklund Transformations”, TMF, 129:2 (2001), 163–183; Theoret. and Math. Phys., 129:2 (2001), 1448

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Teoreticheskaya i Matematicheskaya Fizika, 2001, Volume 129, Number 2, Pages 163–183
DOI: https://doi.org/10.4213/tmf528 (Mi tmf528)

This article is cited in 23 scientific papers (total in 23 papers)

Lagrangian Chains and Canonical Bäcklund Transformations

V. E. Adler^a, V. G. Marikhin^b, A. B. Shabat^b

^a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
^b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Full-text PDF (304 kB) Citations (23)

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DOI: https://doi.org/10.4213/tmf528

Abstract: We consider Darboux transformations for operators of arbitrary order and construct the general theory of Bäcklund transformations based on the Lagrangian formalism. The dressing chain for the Boussinesq equation and its reduction are demonstrative examples for the suggested general theory. We also discuss the well-known Bäcklund transformations for classical soliton equations.

Received: 06.06.2001

English version:
Theoretical and Mathematical Physics, 2001, Volume 129, Issue 2, Pages 1448–1465
DOI: https://doi.org/10.1023/A:1012858820688

Bibliographic databases:

Language: Russian

Citation: V. E. Adler, V. G. Marikhin, A. B. Shabat, “Lagrangian Chains and Canonical Bäcklund Transformations”, TMF, 129:2 (2001), 163–183; Theoret. and Math. Phys., 129:2 (2001), 1448–1465

Citation in format AMSBIB

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https://www.mathnet.ru/eng/tmf528

https://doi.org/10.4213/tmf528

https://www.mathnet.ru/eng/tmf/v129/i2/p163

This publication is cited in the following 23 articles:

Ekaterina Shemyakova, “Classification of Darboux transformations for operators of the form ∂x∂y+a∂x+b∂y+c”, Illinois J. Math., 64:1 (2020)
S. V. Smirnov, “Factorization of Darboux–Laplace transformations for discrete hyperbolic operators”, Theoret. and Math. Phys., 199:2 (2019), 621–636
Caparros Quintero A., Hernandez Heredero R., “Formal Recursion Operators of Integrable Nonevolutionary Equations and Lagrangian Systems”, J. Phys. A-Math. Theor., 51:38 (2018), 385201
G. S. Mauleshova, “The dressing chain and one-point commuting difference operators of rank 1”, Siberian Math. J., 59:5 (2018), 901–908
David Hobby, Ekaterina Shemyakova, “Classification of Multidimensional Darboux Transformations: First Order and Continued Type”, SIGMA, 13 (2017), 010, 20 pp.
Li S., Shemyakova E., Voronov T., “Differential Operators on the Superline, Berezinians, and Darboux Transformations”, Lett. Math. Phys., 107:9 (2017), 1689–1714
Hietarinta J., Joshi N., Nijhoff F., “Discrete Systems and Integrability”, Discrete Systems and Integrability, Cambridge Texts in Applied Mathematics, Cambridge Univ Press, 2016, 1–445
V. G. Marikhin, “Action as an invariant of Bäcklund transformations for Lagrangian systems”, Theoret. and Math. Phys., 184:1 (2015), 953–960
A. B. Shabat, “Simmetricheskie mnogochleny i zakony sokhraneniya”, Vladikavk. matem. zhurn., 14:4 (2012), 83–94
Balakhnev M.Yu., Demskoi D.K., “Auto-Backlund Transformations and Superposition Formulas for Solutions of Drinfeld-Sokolov Systems”, Appl. Math. Comput., 219:8 (2012), 3625–3637
A. B. Shabat, Z. S. El'kanova, “Commuting differential operators”, Theoret. and Math. Phys., 162:3 (2010), 276–285
R. N. Garifullin, A. B. Shabat, “The structure of polynomial conservation laws”, Theoret. and Math. Phys., 161:3 (2009), 1590–1598
A. Shabat, Lecture Notes in Physics, 767, Integrability, 2009, 139
Filipuk, GV, “The symmetric fourth Painlevé hierarchy and associated special polynomials”, Studies in Applied Mathematics, 121:2 (2008), 157
V. E. Adler, A. B. Shabat, “Dressing chain for the acoustic spectral problem”, Theoret. and Math. Phys., 149:1 (2006), 1324–1337
Vsevolod E. Adler, Alexey B. Shabat, “On the One Class of Hyperbolic Systems”, SIGMA, 2 (2006), 093, 17 pp.
Peter A. Clarkson, “Special Polynomials Associated with Rational Solutions of the Painlevé Equations and Applications to Soliton Equations”, Comput. Methods Funct. Theory, 6:2 (2006), 329
S. B. Leble, “Necessary Covariance Conditions for a One-Field Lax Pair”, Theoret. and Math. Phys., 144:1 (2005), 985–994
F. Musso, A. B. Shabat, “Elementary Darboux Transformations and Factorization”, Theoret. and Math. Phys., 144:1 (2005), 1004–1013
A. K. Svinin, “Invariant Submanifolds of the Darboux–Kadomtsev–Petviashvili Chain and an Extension of the Discrete Kadomtsev–Petviashvili Hierarchy”, Theoret. and Math. Phys., 141:2 (2004), 1542–1561

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

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