Geodesic
Algebraic properties of Gardner's deformations for integrable systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 1, pp. 101-117

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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. 
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     author = {A. V. Kiselev},
     title = {Algebraic properties of {Gardner's} deformations for integrable systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {101--117},
     publisher = {mathdoc},
     volume = {152},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a7/}
}
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A. V. Kiselev. Algebraic properties of Gardner's deformations for integrable systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 1, pp. 101-117. http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a7/