Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows
Abstract
We use a Grassmannian framework to define multi-component tau functions as expectation values of certain multi-component Fermi operators satisfying simple bilinear commutation relations on Clifford algebra. The tau functions contain both positive and negative flows and are shown to satisfy the -component KP hierarchy. The hierarchy equations can be formulated in terms of pseudo-differential equations for matrix wave functions derived in terms of tau functions. These equations are cast in form of Sato-Wilson relations. A reduction process leads to the AKNS, two-component Camassa-Holm and Cecotti-Vafa models and the formalism provides simple formulas for their solutions
Keywords
Cite
@article{arxiv.nlin/0605027,
title = {Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows},
author = {Henrik Aratyn and Johan van de Leur},
journal= {arXiv preprint arXiv:nlin/0605027},
year = {2008}
}
Comments
This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/