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Algebraic properties of Gardner's deformations for integrable systems

Arthemy V. Kiselev
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Abstract

An algebraic definition of Gardner's deformations for completely integrable bi-Hamiltonian evolutionary systems is formulated. The proposed approach extends the class of deformable equations and yields new integrable evolutionary and hyperbolic Liouville-type systems. An exactly solvable two-component extension of the Liouville equation is found.

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Arthemy V. Kiselev. 2007-02-10. Algebraic properties of Gardner's deformations for integrable systems. https://doi.org/10.1007/s11232-007-0081-5

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