17 citations · 35 across the 5 of their papers we have counts for
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Loop Algebra Moment Maps and Hamiltonian Models for the Painleve Transcendants
J. Harnad, M. -A. Wisse
The isomonodromic deformations underlying the Painlevé transcendants are interpreted as nonautonomous Hamiltonian systems in the dual $\gR^*$ of a loop algebra $\tilde\grg$ in the…
Moment Maps to Loop Algebras, Classical R-Matrix and Integrable Systems
J. Harnad, M. -A. Wisse
A class of Poisson embeddings of reduced, finite dimensional symplectic vector spaces into the dual space $\Lg_R^*$ of a loop algebra, with Lie Poisson structure determined by the…
Quasi-Periodic Solutions for matrix nonlinear Schroedinger Equations
M. A. Wisse
The Adler-Kostant-Symes theorem yields isospectral hamiltonian flows on the dual $\tilde\grg^{+*}$ of a Lie subalgebra $\tilde\grg^+$ of a loop algebra $\tilde\grg$. A general appr…
Isospectral flow in Loop Algebras and Quasiperiodic Solutions of the Sine-Gordon Equation
J. Harnad, M. -A. Wisse
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 s…
Matrix Nonlinear Schrödinger Equations and Moment Maps into Loop Algebras
J. Harnad, M. -. Wisse
It is shown how Darboux coordinates on a reduced symplectic vector space may be used to parametrize the phase space on which the finite gap solutions of matrix nonlinear Schrödinge…