English

Monodromy free linear equations and many-body systems

Exactly Solvable and Integrable Systems 2023-07-26 v1 Mathematical Physics math.MP

Abstract

We further develop the approach to many-body systems based on finding conditions of existence of meromorphic solutions to certain linear partial differential and difference equations which serve as auxiliary linear problems for nonlinear integrable equations such as KP, BKP, CKP and different versions of the Toda lattice. These conditions imply equations of the time evolution for poles of singular solutions to the nonlinear equations which are equations of motion for integrable many-body systems of Calogero-Moser and Ruijsenaars-Schneider type. A new many-body system is introduced, which governs dynamics of poles of elliptic solutions to the Toda lattice of type B.

Keywords

Cite

@article{arxiv.2211.17216,
  title  = {Monodromy free linear equations and many-body systems},
  author = {I. Krichever and A. Zabrodin},
  journal= {arXiv preprint arXiv:2211.17216},
  year   = {2023}
}

Comments

32 pages, no figures

R2 v1 2026-06-28T07:18:29.294Z