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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 152, Number 1, Pages 101–117
DOI: https://doi.org/10.4213/tmf6073 (Mi tmf6073) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Algebraic properties of Gardner's deformations for integrable systems

A. V. Kiselevab

a Institut des Hautes Études Scientifiques
b Max Planck Institute for Mathematics
Full-text PDF (532 kB) Citations (9)
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DOI: https://doi.org/10.4213/tmf6073
Abstract: We formulate an algebraic definition of Gardner's deformations for completely integrable bi-Hamiltonian evolutionary systems. The proposed approach extends the class of deformable equations and yields new integrable evolutionary and hyperbolic Liouville-type systems. We find an exactly solvable two-component extension of the Liouville equation.
Keywords: Gardner's deformation, integrable family, adjoint system, Hamiltonian, recursion relation.
English version:
Theoretical and Mathematical Physics, 2007, Volume 152, Issue 1, Pages 963–976
DOI: https://doi.org/10.1007/s11232-007-0081-5
Bibliographic databases:
Language: Russian
Citation: A. V. Kiselev, “Algebraic properties of Gardner's deformations for integrable systems”, TMF, 152:1 (2007), 101–117; Theoret. and Math. Phys., 152:1 (2007), 963–976
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6073
  • https://doi.org/10.4213/tmf6073
  • https://www.mathnet.ru/eng/tmf/v152/i1/p101
    • This publication is cited in the following 9 articles:
    1. Kiselev A.V., Krutov A.O., “On the (Non)Removability of Spectral Parameters in Z2-Graded Zero-Curvature Representations and Its Applications”, Acta Appl. Math., 160:1 (2019), 129–167  crossref  mathscinet  isi  scopus
    2. Sergey Ya. Startsev, “Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries”, SIGMA, 13 (2017), 034, 20 pp.  mathnet  crossref
    3. S. Ya. Startsev, “On differential substitutions for evolution systems”, Ufa Math. J., 9:4 (2017), 108–113  mathnet  crossref  isi  elib
    4. Kiseley A.V. Krutov A., “Gardner's Deformations as Generators of New Integrable Systems”, Physics and Mathematics of Nonlinear Phenomena 2013, Journal of Physics Conference Series, 482, IOP Publishing Ltd, 2014, 012021  crossref  isi  scopus
    5. Gomes J.F., Franca G.S., Zimerman A.H., “Nonvanishing boundary condition for the mKdV hierarchy and the Gardner equation”, J. Phys. A: Math. Theor., 45:1 (2012), 015207  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. Kiselev A.V., “Homological Evolutionary Vector Fields in Korteweg-de Vries, Liouville, Maxwell, and Several Other Models”, 7th International Conference on Quantum Theory and Symmetries (QTS7), Journal of Physics Conference Series, 343, IOP Publishing Ltd, 2012, 012058  crossref  isi  scopus
    7. Kiselev A.V. Krutov A.O., “Gardner's Deformations of the Graded Korteweg-de Vries Equations Revisited”, J. Math. Phys., 53:10 (2012), 103511  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    8. A. V. Kiselev, J. W. van de Leur, “Symmetry algebras of Lagrangian Liouville-type systems”, Theoret. and Math. Phys., 162:2 (2010), 149–162  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. Hussin V., Kiselev A.V., Krutov A. ., Wolf T., “N=2 supersymmetric a=4-Korteweg-de Vries hierarchy derived via Gardner's deformation of Kaup-Boussinesq equation”, J. Math. Phys., 51:8 (2010), 083507  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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