Volume 27, Issue 2, January 2020, Pages 324 - 336
Induced Dynamics
Authors
A. K. Pogrebkov
Steklov Mathematical Institute, Gubkin str., 8, Moscow, 119991, Russian Federationpogreb@mi-ras.ruand HSE University, Moscow, Russian Federation
Received 22 June 2019, Accepted 13 October 2019, Available Online 27 January 2020.
- DOI
- 10.1080/14029251.2020.1700648How to use a DOI?
- Keywords
- complete integrability; dynamics of singularities; Calogero–Moser system; Ruijsenaars–Schneider system
- Abstract
Construction of new integrable systems and methods of their investigation is one of the main directions of development of the modern mathematical physics. Here we present an approach based on the study of behavior of roots of functions of canonical variables with respect to a parameter of simultaneous shift of space variables. Dynamics of singularities of the KdV and Sinh–Gordon equations, as well as rational cases of the Calogero–Moser and Ruijsenaars–Schneider models are shown to provide examples of such induced dynamics. Some other examples are given to demonstrates highly nontrivial collisions of particles and Liouville integrability of induced dynamical systems.
- Copyright
- © 2020 The Authors. Published by Atlantis and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
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TY - JOUR AU - A. K. Pogrebkov PY - 2020 DA - 2020/01/27 TI - Induced Dynamics JO - Journal of Nonlinear Mathematical Physics SP - 324 EP - 336 VL - 27 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2020.1700648 DO - 10.1080/14029251.2020.1700648 ID - Pogrebkov2020 ER -