Gardner's deformations as generators of new integrable systems
arXiv:1312.6941 · doi:10.1088/1742-6596/482/1/012021
Abstract
We re-address the problem of construction of new infinite-dimensional completely integrable systems on the basis of known ones, and we reveal a working mechanism for such transitions. By splitting the problem's solution in two steps, we explain how the classical technique of Gardner's deformations facilitates -- in a regular way -- making the first, nontrivial move, in the course of which the drafts of new systems are created (often, of hydrodynamic type). The other step then amounts to higher differential order extensions of symbols in the intermediate hierarchies (e.g., by using the techniques of Dubrovin et al. [1,2] and Ferapontov et al. [3,4]).
Accepted to Proc. Int. workshop 'Physics and Mathematics of Nonlinear Phenomena' (June 22-29, 2013; Gallipoli (LE), Italy), 6 pages
References in corpus (5)
- A simple way of making a Hamiltonian system into a bi-Hamiltonian one
- Classification of integrable super-systems using the SsTools environment
- Algebraic properties of Gardner's deformations for integrable systems
- Gardner's deformations of the N=2 supersymmetric a=4-KdV equation
- Gardner's deformations of the graded Korteweg-de Vries equations revisited