We propose a compact and explicit expression for the solutions of the complexToda chains related to the classical series of simple Lie algebras g. Thesolutions are parametrized by a minimal set of scattering data for thecorresponding Lax matrix. They are expressed as sums over the weight systems ofthe fundamental representations of g and are explicitly covariant under thecorresponding Weyl group action. In deriving these results we start from theMoser formula for the A_r series and obtain the results for the other classicalseries of Lie algebras by imposing appropriate involutions on the scatteringdata. Thus we also show how Moser's solution goes into the one of Olshanetskyand Perelomov. The results for the large-time asymptotics of the A_r -CTCsolutions are extended to the other classical series B_r - D_r. We exhibit alsosome `irregular' solutions for the D_{2n+1} algebras whose asymptotic regimesat t ->\pm\infty are qualitatively different. Interesting examples of boundedand periodic solutions are presented and the relations between the solutionsfor the algebras D_4, B_3 and G_2 $ are analyzed.
展开▼
