Isospectral flow in Loop Algebras and Quasiperiodic Solutions of the Sine-Gordon Equation

Details Isospectral flow in Loop Algebras and Quasiperiodic Solutions of the Sine-Gordon Equation Isospectral flow in Loop Algebras and Quasiperiodic Solutions of the Sine-Gordon Equation

1992-10-14

arxiv.org/abs/hep-th/9210077v1

J.Math.Phys. 34 (1993) 3518-3526

Physics

High Energy Physics

High Energy Physics - Theory

12 pgs

Scientific paper

10.1063/1.530041

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 $\grg^*$ of a loop algebra $\grg$, is parametrized by a finite dimensional symplectic vector space $W$ embedded into $\grg^*$ 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.

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