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

L. V. Bogdanov, B. G. Konopelchenko
1998 Journal of Mathematical Physics  
Analytic-bilinear approach for construction and study of integrable hierarchies is discussed. Generalized multicomponent KP and 2D Toda lattice hierarchies are considered. This approach allows to represent generalized hierarchies of integrable equations in a condensed form of finite functional equations. Generalized hierarchy incorporates basic hierarchy, modified hierarchy, singularity manifold equation hierarchy and corresponding linear problems. Different levels of generalized hierarchy are
more » ... onnected via invariants of Combescure symmetry transformation. Resolution of functional equations also leads to the τ -function and addition formulae to it.
doi:10.1063/1.532531 fatcat:s2qrhpw55vedfeghlvjdc2lfra