Algebraic properties of Gardner's deformations for integrable systems

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.

Proc. conf. "Nonlinear Physics: Theory and Experiment IV" (Gallipoli, 2006); Theor. Math. Phys. (2007) 151:3/152:1-2, 16p. (to appear)

References in corpus (6)

• Hamiltonian operators and l*-coverings
• Coverings and fundamental algebras for partial differential equations
• Integrable Systems and Metrics of Constant Curvature
• On Hamiltonian flows on Euler-type equations
• On application of Liouville type equations to constructing Bäcklund transformations
• Gardner's deformations of the Boussinesq equations

Cited by in corpus (8)

• Symmetry algebras of Lagrangian Liouville-type systems
• Nonvanishing boundary condition for the mKdV hierarchy and the Gardner equation
• Gardner's deformations of the N=2 supersymmetric a=4-KdV equation
• Gardner's deformations of the graded Korteweg-de Vries equations revisited
• Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries
• Homological evolutionary vector fields in Korteweg-de Vries, Liouville, Maxwell, and several other models
• On the (non)removability of spectral parameters in $Z_2$-graded zero-curvature representations and its applications
• Gardner's deformations as generators of new integrable systems