Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies

摘要

Analytic-bilinear approach for construction and study of integrablehierarchies is discussed. Generalized multicomponent KP and 2D Toda latticehierarchies are considered. This approach allows to represent generalizedhierarchies of integrable equations in a condensed form of finite functionalequations. Generalized hierarchy incorporates basic hierarchy, modifiedhierarchy, singularity manifold equation hierarchy and corresponding linearproblems. Different levels of generalized hierarchy are connected viainvariants of Combescure symmetry transformation. Resolution of functionalequations also leads to the $\tau $-function and addition formulae to it.