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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/tmf/v152/i1/p101
    • This publication is cited in the following 9 articles:
    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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    References:66
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