Isospectral flow in loop algebras and quasiperiodic solutions of the sine-Gordon equation

Journal Article · Sun Aug 01 00:00:00 EDT 1993 · Journal of Mathematical Physics (New York); (United States)

DOI:https://doi.org/10.1063/1.530041· OSTI ID:5567419

Harnad, J ^[1]; Wisse, M ^[2]

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1. Department of Mathematics and Statistics, Concordia University, Montreal, PQ (Canada) Centre de recherches mathematiques, Universite de Montreal, C.P. 6128-A, Montreal, PQ (Canada)
2. Departement de mathematiques et de statistique, Universite de Montreal, C.P. 6128-A, Montreal, PQ (Canada)

The sine-Gordon equation is considered in the Hamiltonian framework provided by the Adler--Kostant--Symes theorem. The phase space, a finite dimensional coadjoint orbit in the dual space g* of a loop algebra g, is parameterized by a finite dimensional symplectic vector space [ital W] embedded into g* by a moment map. Real quasiperiodic solutions are computed in terms of theta functions using a Liouville generating function which generates a canonical transformation to linear coordinates on the Jacobi variety of a suitable hyperelliptic curve.

• OSTI ID: 5567419
• Journal Information: Journal of Mathematical Physics (New York); (United States), Vol. 34:8; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
SINE-GORDON EQUATION
HAMILTONIANS
CANONICAL TRANSFORMATIONS
COORDINATES
PHASE SPACE
EQUATIONS
FIELD EQUATIONS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
QUANTUM OPERATORS
SPACE
TRANSFORMATIONS
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)