Matrix Nonlinear Schrödinger Equations and Moment Maps into Loop Algebras${}^†$

Details Matrix Nonlinear Schrödinger Equations and Moment Maps into Loop Algebras${}^†$ Matrix Nonlinear Schrödinger Equations and Moment Maps into Loop Algebras${}^†$

1992-10-13

arxiv.org/abs/hep-th/9210071v1

J.Math.Phys. 33 (1992) 4164-4176

Physics

High Energy Physics

High Energy Physics - Theory

17 pgs, plus 4 Tables Preprint CRM-1831

Scientific paper

10.1063/1.529815

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 Schr\"odinger equations are realized as isospectral Hamiltonian flows. The parametrization follows from a moment map embedding of the symplectic vector space, reduced by suitable group actions, into the dual $\tilde\grg^{+*}$ of the algebra $\tilde\grg^+$ of positive frequency loops in a Lie algebra $\grg$. The resulting phase space is identified with a Poisson subspace of $\tilde\grg^{+*}$ consisting of elements that are rational in the loop parameter. Reduced coordinates associated to the various Hermitian symmetric Lie algebras $(\grg,\grk)$ corresponding to the classical Lie algebras are obtained.

Affiliated with

Also associated with

No associations

Rating

Matrix Nonlinear Schrödinger Equations and Moment Maps into Loop Algebras${}^†$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Matrix Nonlinear Schrödinger Equations and Moment Maps into Loop Algebras${}^†$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Matrix Nonlinear Schrödinger Equations and Moment Maps into Loop Algebras${}^†$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-510109