Gardner's deformations of the Boussinesq equations

Abstract

Using the algebraic method of Gardner's deformations for completely integrable systems, we construct the recurrence relations for densities of the Hamiltonians for the Boussinesq and the Kaup-Boussinesq equations. By extending the Magri schemes for these systems, we obtain new integrable equations adjoint with respect to the initial ones and describe their Hamiltonian structures and symmetry properties.

Proc. Workshop `Quantizaion, Dualities, and Integrable Systems,' 23-27 January 2006, Pamukkale University, Turkey; 7 pages. MSC 35Q53, 37K05, 37K10, 37K35

References in corpus (4)

• Classification of polynomial integrable systems of mixed scalar and vector evolution equations. I
• Why nonlocal recursion operators produce local symmetries: new results and applications
• The Gardner Category and Non-local Conservation Laws for N=1 Super KdV
• On Hamiltonian flows on Euler-type equations

Cited by in corpus (3)

• Algebraic properties of Gardner's deformations for integrable systems
• Gardner's deformations of the N=2 supersymmetric a=4-KdV equation
• Gardner's deformations as generators of new integrable systems