Gardner's deformations as generators of new integrable systems
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]).
Cite
@article{arxiv.1312.6941,
title = {Gardner's deformations as generators of new integrable systems},
author = {Arthemy V. Kiselev and Andrey O. Krutov},
journal= {arXiv preprint arXiv:1312.6941},
year = {2014}
}
Comments
Accepted to Proc. Int. workshop 'Physics and Mathematics of Nonlinear Phenomena' (June 22-29, 2013; Gallipoli (LE), Italy), 6 pages