Hypergeometric Functions as Infinite-Soliton Tau Functions |
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Authors: | A Yu Orlov |
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Institution: | (1) Shirshov Oceanology Institute, RAS, Moscow, Russia |
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Abstract: | 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.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 2, pp. 222–250, February, 2006. |
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Keywords: | solitons rational solutions tau function hypergeometric function duality |
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