|XXXV Workshop on Geometric Methods in Physics
Soliton hierarchies and matrix loop algebras
We will talk about the zero curvature formulation for soliton hierarchies associated with matrix spectral problems. Liouville integrability will be shown by establishing Hamiltonian structures through either the trace identity or the variational identity over matrix loop algebras. Illustrative examples are generated from matrix spectral problems formulated using the two real three dimensional Lie algebras, sl(2,R) and so(3,R).