What does integrability of finite-gap or soliton potentials mean?

DOI10.1098/rsta.2007.2056zbMath1153.37411arXivnlin/0505003OpenAlexW2148344111WikidataQ51911712 ScholiaQ51911712MaRDI QIDQ5503944

Yurii V. Brezhnev

Publication date: 21 January 2009

Published in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0505003

zbMATH Keywords

finite-gap integrationalgebraic-geometric methodsAbelian integralsintegrability by quadratures\(\Theta \)-functionsriccati's equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Soliton equations (35Q51) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (7)

On classical symmetries of ordinary differential equations related to stationary integrable partial differential equations ⋮ Differential Galois theory and Darboux transformations for integrable systems ⋮ Integrability of the one dimensional Schrödinger equation ⋮ Picard-Vessiot theory and integrability ⋮ Tau functions associated with linear systems ⋮ Rational KdV potentials and differential Galois theory ⋮ Elliptic solitons, Fuchsian equations, and algorithms

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