Induced dynamics. (English) Zbl 1436.37081
Summary: 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.
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 35Q51 | Soliton equations |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
Keywords:
complete integrability; dynamics of singularities; Calogero-Moser system; Ruijsenaars-Schneider systemReferences:
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