Non-autonomous soliton hierarchies
Exactly Solvable and Integrable Systems
2024-07-12 v1 Mathematical Physics
math.MP
Abstract
A formalism of systematic construction of integrable non-autonomous deformations of soliton hierarchies is presented. The theory is formulated as an initial value problem (IVP) for an associated Frobenius integrability condition on a Lie algebra. It is showed that this IVP has a formal solution and within the framewrok of two particular subalgebras of the hereditary Lie algebra the explicit forms of this formal solution are presented. Finally, this formalism is applied to Korteveg-de Vries, dispersive water waves and Ablowitz-Kaup-Newell-Segur soliton hierarchies.
Cite
@article{arxiv.2407.08656,
title = {Non-autonomous soliton hierarchies},
author = {Maciej Błaszak and Krzysztof Marciniak and Błażej M. Szablikowski},
journal= {arXiv preprint arXiv:2407.08656},
year = {2024}
}
Comments
25 pages