Quantizations and integrable systems

DOI10.1007/BF00417226zbMath0715.58015OpenAlexW2082263682MaRDI QIDQ752568

Boris A. Kupershmidt

Publication date: 1990

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00417226

zbMATH Keywords

quantizationKdVBoussinesq and KP equationsdeformation theory of rings and algebrasintegrable hamiltonian systems

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Geometry and quantization, symplectic methods (81S10) Deformations of associative rings (16S80) Geometric quantization (53D50)

Related Items

On the integrability of a third-order Monge-Ampère type equation. ⋮ Multidimensional integrable systems and deformations of Lie algebra homomorphisms ⋮ A geometry for multidimensional integrable systems ⋮ \(W_n^{(\kappa)}\) algebra associated with the Moyal KdV hierarchy ⋮ Properties of Moyal-Lax representation ⋮ Collisionless Boltzmann equations and integrable moment equations ⋮ Phase space quantum mechanics ⋮ Virasoro action on pseudo-differential symbols and (noncommutative) supersymmetric peakon type integrable systems ⋮ On the Moyal Quantized BKP Type Hierarchies

Cites Work

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• Algebraic aspects of nonlinear differential equations
• Modifying Lax equations and the second Hamiltonian structure
• Deformation theory and quantization. I: Deformations of symplectic structures
• Mathematics of dispersive water waves
• Lie Group Dynamical Formalism and the Relation between Quantum Mechanics and Classical Mechanics

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