Abstract
Relates equivalence classes of coupled systems of N linear wave equations to motions of an N*N matrix dynamical systems, the two-dimensional non-Abelian Toda lattice. In particular, the correspondence is shown to relate those coupled systems of wave equations with progressing-wave general solutions to motions of the finite non-Abelian Toda lattice with free ends, generalizing a known result for the N=1 case. Some non-trivial motions of such Toda lattices are found, and the corresponding coupled wave equations and their progressing wave general solutions are given. Other consequences of the correspondence and possible application of the progressing waves are discussed.