Iso-spectral deformations of general matrix and their reductions on Lie algebras

Details Iso-spectral deformations of general matrix and their reductions on Lie algebras Iso-spectral deformations of general matrix and their reductions on Lie algebras

1995-07-03

arxiv.org/abs/solv-int/9506005v1

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, AMSLaTex

Scientific paper

10.1007/BF02108824

We study an iso-spectral deformation of general matrix which is a natural generalization of the Toda lattice equation. We prove the integrability of the deformation, and give an explicit formula for the solution to the initial value problem. The formula is obtained by generalizing the orthogonalization procedure of Szeg\"{o}. Based on the root spaces for simple Lie algebras, we consider several reductions of the hierarchy. These include not only the integrable systems studied by Bogoyavlensky and Kostant, but also their generalizations which were not known to be integrable before. The behaviors of the solutions are also studied. Generically, there are two types of solutions, having either sorting property or blowing up to infinity in finite time.

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