Journal of Nonlinear Mathematical Physics

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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 2
Pages
324 - 336
Publication Date
2020/01/27
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2020.1700648How to use a DOI?
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/).

Cite this article

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  -