ANALYTIC-BILINEAR APPROACH TO INTEGRABLE HIERARCHIES - II - MULTICOMPONENT KP AND 2D TODA LATTICE HIERARCHIES

An analytic-bilinear approach for the construction and study of integr able hierarchies is discussed. Generalized multicomponent KP and 2D To da lattice hierarchies are considered. This approach allows us to repr esent generalized hierarchies of integrable equations in a condensed f orm of finite functional equations. A generalized hierarchy incorporat es basic hierarchy, modified hierarchy, singularity manifold equation hierarchy, and corresponding linear problems. Different levels of gene ralized hierarchy are connected via invariants of Combescure symmetry transformation. The resolution of functional equations also leads to t he tau function, and addition formulas to it. (C) 1998 American Instit ute of Physics.