Non-Noether symmetries in Hamiltonian Dynamical Systems

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dc.creatorChavchanidze, George
dc.date2004-05-03
dc.date.accessioned2026-07-07T04:31:09Z
dc.date.available2026-07-07T04:31:09Z
dc.descriptionWe discuss geometric properties of non-Noether symmetries and their possible applications in integrable Hamiltonian systems. Correspondence between non-Noether symmetries and conservation laws is revisited. It is shown that in regular Hamiltonian systems such a symmetries canonically lead to a Lax pairs on the algebra of linear operators on cotangent bundle over the phase space. Relationship between the non-Noether symmetries and other wide spread geometric methods of generating conservation laws such as bi-Hamiltonian formalism, bidifferential calculi and Frolicher-Nijenhuis geometry is considered. It is proved that the integrals of motion associated with the continuous non-Noether symmetry are in involution whenever the generator of the symmetry satisfies a certain Yang-Baxter type equation. Action of one-parameter group of symmetry on algebra of integrals of motion is studied and involutivity of group orbits is discussed. Hidden non-Noether symmetries of Toda chain, nonlinear Schrodinger equation, Korteweg-de Vries equations, Benney system, nonlinear water wave equations and Broer-Kaup system are revealed and discussed.
dc.descriptionLaTeX 2e, 75 pages, no figures
dc.identifierhttps://arxiv.org/abs/math-ph/0405003
dc.identifierhttp://arxiv.org/abs/math-ph/0405003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57718
dc.subjectMathematical Physics
dc.subjectDynamical Systems
dc.subjectSymplectic Geometry
dc.subject70H33; 70H06; 58J70; 53Z05; 35A30
dc.titleNon-Noether symmetries in Hamiltonian Dynamical Systems
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