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Algebraic properties of Gardner’s deformations for integrable systems

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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.

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Authors and Affiliations

  1. Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111, Bonn, Germany

    A. V. Kiselev

  2. Institut des Hautes Études Scientifiques, Le Bois-Marie 35, Route de Chartres, F-91440, Bures-sur-Yvette, France

    A. V. Kiselev

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  1. A. V. Kiselev
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 1, pp. 101–117, July, 2007.

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Kiselev, A.V. Algebraic properties of Gardner’s deformations for integrable systems. Theor Math Phys 152, 963–976 (2007). https://doi.org/10.1007/s11232-007-0081-5

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