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arXiv · hep-th/9210077

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

J. Harnad·M. -A. Wisse
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Abstract

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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J. Harnad, M. -A. Wisse. 1992-10-14. Isospectral flow in Loop Algebras and Quasiperiodic Solutions of the Sine-Gordon Equation. https://doi.org/10.1063/1.530041

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