English

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.

Keywords

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

R2 v1 2026-06-28T17:37:38.481Z