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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
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.
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
Linking options:
https://www.mathnet.ru/eng/tmf6073https://doi.org/10.4213/tmf6073 https://www.mathnet.ru/eng/tmf/v152/i1/p101
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