2013
DOI: 10.4236/am.2013.410a3013
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Hidden Symmetries of Lax Integrable Nonlinear Systems

Abstract: Recently devised new symplectic and differential-algebraic approaches to studying hidden symmetry properties of nonlinear dynamical systems on functional manifolds and their relationships to Lax integrability are reviewed. A new symplectic approach to constructing nonlinear Lax integrable dynamical systems by means of Lie-algebraic tools and based upon the Marsden-Weinstein reduction method on canonically symplectic manifolds with group symmetry, is described. Its natural relationship with the well-known Adler… Show more

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Cited by 4 publications
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“…for all elements a, b ∈G. The following theorem, defining the related Poisson structure [10,12,45,48] on the adjoint spaceG holds.…”
Section: Introductionmentioning
confidence: 99%
“…for all elements a, b ∈G. The following theorem, defining the related Poisson structure [10,12,45,48] on the adjoint spaceG holds.…”
Section: Introductionmentioning
confidence: 99%