Quasi-symmetric functions and the KP hierarchy

Details Quasi-symmetric functions and the KP hierarchy Quasi-symmetric functions and the KP hierarchy

2009-01-16

arxiv.org/abs/0901.2562v2

Physics

Mathematical Physics

16 pages

Scientific paper

Quasi-symmetric functions show up in an approach to solve the Kadomtsev-Petviashvili (KP) hierarchy. This moreover features a new nonassociative product of quasi-symmetric functions that satisfies simple relations with the ordinary product and the outer coproduct. In particular, supplied with this new product and the outer coproduct, the algebra of quasi-symmetric functions becomes an infinitesimal bialgebra. Using these results we derive a sequence of identities in the algebra of quasi-symmetric functions that are in formal correspondence with the equations of the KP hierarchy.

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