Matches in SemOpenAlex for { <https://semopenalex.org/work/W2121945070> ?p ?o ?g. }
Showing items 1 to 90 of
90
with 100 items per page.
- W2121945070 endingPage "522" @default.
- W2121945070 startingPage "455" @default.
- W2121945070 abstract "Abstract The following observation, due to E. Trubowitz, illustrates an intimate relationship between spectral theory and Hamiltonian mechanics in the presence of constraints. Let q(s) be a real periodic function such that the Hill operator, magnified image has only a finite number g R of simple eigenvalues. There exist g R + 1 periodic eigenfunctions x 1 ,…, x and corresponding eigenvalues a 1 ,…, a of L such that magnified image where y r = dx r / ds . The equations Lx r = a r x r , r = 1,…,g R +1, make up the classical Neumann system, a system of harmonic oscillators constrained to the unit sphere. H. Flaschka obtained similar results about the Neumann system from a more general point of view. His assumption, that there exists an operator of odd order that commutes with L, leads to algebraic curve theory by the method of Krichever and from there to the Neumann formulas above. The familiar Lax pairs, the constants of motion and the quadrics of the Neumann system emerge as consequences of the Riemann‐Roch theoreni. The existence of isospectral deformations of L, the Korteweg de‐Vries hierarchy of the soliton equations, underlies the complete integrability of the Neumann system. This paper extends Flaschka's techniques, replacing L by an operator of order n 2 2. Higher Neumann systems are defined in a way that leads naturally to interesting symplectic manifolds, Lax pairs and integrals of motion. C. Tomei, using scattering theory, obtained some of our n = 3 formulas." @default.
- W2121945070 created "2016-06-24" @default.
- W2121945070 creator A5006982236 @default.
- W2121945070 date "1987-07-01" @default.
- W2121945070 modified "2023-09-27" @default.
- W2121945070 title "Generalizations of the neumann system a curve-theoretical approach-part I" @default.
- W2121945070 cites W1966021537 @default.
- W2121945070 cites W1971888971 @default.
- W2121945070 cites W1980138746 @default.
- W2121945070 cites W1994463325 @default.
- W2121945070 cites W1996834583 @default.
- W2121945070 cites W2010528264 @default.
- W2121945070 cites W2023620134 @default.
- W2121945070 cites W2025120160 @default.
- W2121945070 cites W2070167942 @default.
- W2121945070 cites W2104369108 @default.
- W2121945070 cites W2136384750 @default.
- W2121945070 cites W2159695001 @default.
- W2121945070 cites W2981083573 @default.
- W2121945070 cites W4205727720 @default.
- W2121945070 cites W4229938736 @default.
- W2121945070 cites W4236651295 @default.
- W2121945070 cites W4246274074 @default.
- W2121945070 cites W4248431629 @default.
- W2121945070 cites W69264405 @default.
- W2121945070 doi "https://doi.org/10.1002/cpa.3160400405" @default.
- W2121945070 hasPublicationYear "1987" @default.
- W2121945070 type Work @default.
- W2121945070 sameAs 2121945070 @default.
- W2121945070 citedByCount "13" @default.
- W2121945070 countsByYear W21219450702015 @default.
- W2121945070 crossrefType "journal-article" @default.
- W2121945070 hasAuthorship W2121945070A5006982236 @default.
- W2121945070 hasConcept C104317684 @default.
- W2121945070 hasConcept C121332964 @default.
- W2121945070 hasConcept C121770821 @default.
- W2121945070 hasConcept C128803854 @default.
- W2121945070 hasConcept C134306372 @default.
- W2121945070 hasConcept C158448853 @default.
- W2121945070 hasConcept C158693339 @default.
- W2121945070 hasConcept C17020691 @default.
- W2121945070 hasConcept C172829509 @default.
- W2121945070 hasConcept C185592680 @default.
- W2121945070 hasConcept C200741047 @default.
- W2121945070 hasConcept C202444582 @default.
- W2121945070 hasConcept C2779710842 @default.
- W2121945070 hasConcept C33923547 @default.
- W2121945070 hasConcept C37914503 @default.
- W2121945070 hasConcept C55493867 @default.
- W2121945070 hasConcept C62520636 @default.
- W2121945070 hasConcept C86339819 @default.
- W2121945070 hasConceptScore W2121945070C104317684 @default.
- W2121945070 hasConceptScore W2121945070C121332964 @default.
- W2121945070 hasConceptScore W2121945070C121770821 @default.
- W2121945070 hasConceptScore W2121945070C128803854 @default.
- W2121945070 hasConceptScore W2121945070C134306372 @default.
- W2121945070 hasConceptScore W2121945070C158448853 @default.
- W2121945070 hasConceptScore W2121945070C158693339 @default.
- W2121945070 hasConceptScore W2121945070C17020691 @default.
- W2121945070 hasConceptScore W2121945070C172829509 @default.
- W2121945070 hasConceptScore W2121945070C185592680 @default.
- W2121945070 hasConceptScore W2121945070C200741047 @default.
- W2121945070 hasConceptScore W2121945070C202444582 @default.
- W2121945070 hasConceptScore W2121945070C2779710842 @default.
- W2121945070 hasConceptScore W2121945070C33923547 @default.
- W2121945070 hasConceptScore W2121945070C37914503 @default.
- W2121945070 hasConceptScore W2121945070C55493867 @default.
- W2121945070 hasConceptScore W2121945070C62520636 @default.
- W2121945070 hasConceptScore W2121945070C86339819 @default.
- W2121945070 hasIssue "4" @default.
- W2121945070 hasLocation W21219450701 @default.
- W2121945070 hasOpenAccess W2121945070 @default.
- W2121945070 hasPrimaryLocation W21219450701 @default.
- W2121945070 hasRelatedWork W1490705187 @default.
- W2121945070 hasRelatedWork W1994604058 @default.
- W2121945070 hasRelatedWork W2011610704 @default.
- W2121945070 hasRelatedWork W2020845165 @default.
- W2121945070 hasRelatedWork W2028672743 @default.
- W2121945070 hasRelatedWork W2050309183 @default.
- W2121945070 hasRelatedWork W3135293428 @default.
- W2121945070 hasRelatedWork W3139795425 @default.
- W2121945070 hasRelatedWork W3145291484 @default.
- W2121945070 hasRelatedWork W4230609988 @default.
- W2121945070 hasVolume "40" @default.
- W2121945070 isParatext "false" @default.
- W2121945070 isRetracted "false" @default.
- W2121945070 magId "2121945070" @default.
- W2121945070 workType "article" @default.