Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2006-05-12
SIGMA 3 (2007), 020, 29 pages
Nonlinear Sciences
Exactly Solvable and Integrable Systems
This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Sym
Scientific paper
10.3842/SIGMA.2007.020
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 $2n$-component KP hierarchy. The hierarchy equations can be formulated in terms of pseudo-differential equations for $n \times n$ 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
Aratyn Henrik
de Leur Johan van
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