Towards an algebro-geometric interpretation of the Neumann system
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Publication:1069059
DOI10.2748/tmj/1178228807zbMath0582.35102OpenAlexW1996834583MaRDI QIDQ1069059
Publication date: 1984
Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2748/tmj/1178228807
quadratic potentialconstants of motionLax equationsaffine curve linebundleBurchnall-Chaundy-Krichever theoryNeumann's system
General topics in linear spectral theory for PDEs (35P05) Partial differential equations of mathematical physics and other areas of application (35Q99) Curves in algebraic geometry (14H99)
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New factorization of the Kaup-Newell hierarchy, Generalizations of the Neumann system, Isospectral Hamiltonian flows in finite and infinite dimensions. I: Generalized Moser systems and moment maps into loop algebras, Generalizations of the neumann system a curve theoretical approach-part II, Geodesic flows and Neumann systems on Stiefel varieties: geometry and integrability, The generalized Neumann hierarchy associated with the energy dependent Schrödinger equation, Quasi-periodic solutions of the integrable dynamical systems related to Hill's equation, Finite-gap solutions of 2+1 dimensional integrable nonlinear evolution equations generated by the Neumann systems, Darboux coordinates and Liouville-Arnold integration in loop algebras, Integrability of Adler's discretization of the Neumann system
Cites Work
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- Completely integrable systems, Euclidean Lie algebras, and curves
- The spectrum of Hill's equation
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- The C. Neumann Problem as a Completely Integrable System on an Adjoint Orbit
- Geodesics on quadrics and a mechanical problem of C. Neumann.
- Korteweg‐devries equation and generalizations. VI. methods for exact solution
- Transversal Homoclinic Orbits in an Integrable System
- Commutative ordinary differential operators. II.—The identity P n = Q m
- Nonlinear wave equations and constrained harmonic motion
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