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- W2950224970 abstract "We consider a special class of solutions of the BKP hierarchy which we call $tau$-functions of hypergeometric type. These are series in Schur $Q$-functions over partitions, with coefficients parameterised by a function of one variable $xi$, where the quantities $xi(k)$, $kinmathbb{Z^+}$, are integrals of motion of the BKP hierarchy. We show that this solution is, at the same time, a infinite soliton solution of a dual BKP hierarchy, where the variables $xi(k)$ are now related to BKP higher times. In particular, rational solutions of the BKP hierarchy are related to (finite) multi-soliton solution of the dual BKP hierarchy. The momenta of the solitons are given by the parts of partitions in the Schur $Q$-function expansion of the $tau$-function of hypergeometric type. We also show that the KdV and the NLS soliton $tau$-functions coinside the BKP $tau$-functions of hypergeometric type, evaluated at special point of BKP higher time; the variables $xi$ (which are BKP integrals of motions) being related to KdV and NLS higher times." @default.
- W2950224970 created "2019-06-27" @default.
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- W2950224970 date "2004-05-06" @default.
- W2950224970 modified "2023-09-27" @default.
- W2950224970 title "A relationship between rational and multi-soliton solutions of the BKP hierarchy" @default.
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