NDLI: Remarks on integrable systems

Content Provider	Springer Nature Link
Author	Kozlov, Valery V.
Copyright Year	2014
Abstract	The problem of integrability conditions for systems of differential equations is discussed. Darboux’s classical results on the integrability of linear non-autonomous systems with an incomplete set of particular solutions are generalized. Special attention is paid to linear Hamiltonian systems. The paper discusses the general problem of integrability of the systems of autonomous differential equations in an n-dimensional space, which admit the algebra of symmetry fields of dimension ⩽ n. Using a method due to Liouville, this problem is reduced to investigating the integrability conditions for Hamiltonian systems with Hamiltonians linear in the momenta in phase space of dimension that is twice as large. In conclusion, the integrability of an autonomous system in three-dimensional space with two independent non-trivial symmetry fields is proved. It should be emphasized that no additional conditions are imposed on these fields.
Starting Page	145
Ending Page	161
Page Count	17
File Format	PDF
ISSN	15603547
Journal	Regular and Chaotic Dynamics
Volume Number	19
Issue Number	2
e-ISSN	14684845
Language	English
Publisher	Pleiades Publishing
Publisher Date	2014-04-04
Publisher Place	Moscow
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	integrability by quadratures adjoint system Hamiltonian equations Euler — Jacobi theorem Lie theorem symmetries Dynamical Systems and Ergodic Theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Statistical and Nonlinear Physics Mathematical Physics Mechanical Engineering Modeling and Simulation

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