Quasi-symmetric functions and the KP hierarchy |
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Authors: | Aristophanes Dimakis |
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Institution: | a Department of Financial and Management Engineering, University of the Aegean, 31 Fostini Street, GR-82100 Chios, Greece b Max-Planck-Institute for Dynamics and Self-Organization, Bunsenstrasse 10, D-37073 Göttingen, Germany |
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Abstract: | Quasi-symmetric functions arise 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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Keywords: | 16W30 05E05 37K10 17Dxx |
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