Rational solutions of the full Kostant-Toda equation.

Abstract

In this paper a commuting hierarchy of flows including the full Kostant-Toda equation is studied. A Mulase’s approach which uses the so-called Borel-Gauss decomposition leads to explicit rational solutions of the full Kostant-Toda equation. Finally, we investigate how the solution blows up in finite time in the case of matrices of order 2.