caa a22 4500 46791060X CHVBK 20180406152848.0 cr unu---uuuuu 170328e20060201xx s 000 0 eng 10.1007/s11232-006-0018-4 doi (NATIONALLICENCE)springer-10.1007/s11232-006-0018-4 Orlov A. Shirshov Oceanology Institute, RAS, Moscow, Russia aut Hypergeometric Functions as Infinite-Soliton Tau Functions [Elektronische Daten] [A. Orlov] It is known that resonant multisoliton solutions depend on higher times and a set of parameters (integrals of motion). We show that soliton tau functions of the Toda lattice (and of the multicomponent Toda lattice) are tau functions of a dual hierarchy, where the higher times and the parameters (integrals of motion) exchange roles. The multisoliton solutions turn out to be rational solutions of the dual hierarchy, and the infinite-soliton tau functions turn out to be hypergeometric-type tau functions of the dual hierarchy. The variables in the dual hierarchies exchange roles. Soliton momenta are related to the Frobenius coordinates of partitions in the decomposition of rational solutions with respect to Schur functions. As an example, we consider partition functions of matrix models: their perturbation series is, on one hand, a hypergeometric tau function and, on the other hand, can be interpreted as an infinite-soliton solution. Springer Science+Business Media, Inc., 2006 solitons nationallicence rational solutions nationallicence tau function nationallicence hypergeometric function nationallicence duality nationallicence Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 146/2(2006-02-01), 183-206 0040-5779 146:2<183 2006 146 11232 https://doi.org/10.1007/s11232-006-0018-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11232-006-0018-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Orlov A. Shirshov Oceanology Institute, RAS, Moscow, Russia aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 146/2(2006-02-01), 183-206 0040-5779 146:2<183 2006 146 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer