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• W3104453914 endingPage "226" @default.
• W3104453914 startingPage "217" @default.
• W3104453914 abstract "Variation of coupling constants of integrable system can be considered as canonical transformation or, infinitesimally, a Hamiltonian flow in the space of such systems. Any function T(p→,q→) generates a one-parametric family of integrable systems in vicinity of a single system: this gives an idea of how many integrable systems there are in the space of coupling constants. Inverse flow is generated by a dual “Hamiltonian”, T(p→,q→) associated with the dual integrable system. In vicinity of a self-dual point the duality transformation just interchanges momenta and coordinates in such a “Hamiltonian”: T(p→,q→)=T(q→,p→). For integrable system with several coupling constants the corresponding “Hamiltonians” Ti(p→,q→) satisfy Whitham equations and after quantization (of the original system) become operators satisfying the zero-curvature condition in the space of coupling constants: ∂∂ga −T a( p→ ̂, q→ ̂),∂∂gb −T b( p→ ̂, q→ ̂) =0. Some explicit formulas are given for harmonic oscillator and for Calogero–Ruijsenaars–Dell system." @default.
• W3104453914 created "2020-11-23" @default.
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• W3104453914 date "2002-01-01" @default.
• W3104453914 modified "2023-09-23" @default.
• W3104453914 title "p,q-Duality and Hamiltonian flows in the space of integrable systems or integrable systems as canonical transforms of the free ones" @default.
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• W3104453914 doi "https://doi.org/10.1016/s0370-2693(01)01267-9" @default.
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