Expansions with respect to squares, symplectic and poisson structures associated with the Sturm-Liouville problem. II

The concept of tangent vector is made more precise to meet the specific nature of the Sturm-Liouville problem, and on this basis a Poisson bracket that is modified compared with the Gardner form by special boundary terms is derived from the Zakharov-Faddeev symplectic form. This bracket is nondegene...

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Veröffentlicht in:	Theor. Math. Phys.; (United States) 1988-05, Vol.75 (2), p.448-460
Hauptverfasser:	Arkad'ev, V. A., Pogrebkov, A. K., Polivanov, M. K.
Format:	Artikel
Sprache:	eng
Schlagworte:	645201 - High Energy Physics- Particle Interactions & Properties-Theoretical- General & Scattering Theory ANNIHILATION OPERATORS BOUNDARY CONDITIONS DIFFERENTIAL EQUATIONS EQUATIONS FOURIER TRANSFORMATION HAMILTONIANS INTEGRAL TRANSFORMATIONS INVARIANCE PRINCIPLES KORTEWEG-DE VRIES EQUATION LIE GROUPS MAPPING MATHEMATICAL MANIFOLDS MATHEMATICAL OPERATORS PARTIAL DIFFERENTIAL EQUATIONS PHYSICS OF ELEMENTARY PARTICLES AND FIELDS POISSON EQUATION QUANTUM OPERATORS SCATTERING SERIES EXPANSION SP GROUPS STURM-LIOUVILLE EQUATION SYMMETRY GROUPS TENSORS TOPOLOGICAL MAPPING TRANSFORMATIONS VECTORS
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Zusammenfassung:	The concept of tangent vector is made more precise to meet the specific nature of the Sturm-Liouville problem, and on this basis a Poisson bracket that is modified compared with the Gardner form by special boundary terms is derived from the Zakharov-Faddeev symplectic form. This bracket is nondegenerate, and in it the variables of the discrete and continuous spectra are separated.
ISSN:	0040-5779 1573-9333
DOI:	10.1007/BF01017483