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ON A GENERALIZED TZITZEICA EQUATION

Published online by Cambridge University Press:  14 July 2005

RALPH WILLOX
RALPH WILLOX
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, 153-8914 Tokyo, Japan e-mail: willox@poisson.ms.u-tokyo.ac.jp
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Abstract

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Extending the so called coupled KP hierarchy to negative time flows one obtains coupled Toda-type equations defined on a two-dimensional lattice. These equations allow for reductions to 1+1 dimensional integrable systems that are defined on a finite part of this lattice. A system of coupled Hirota bilinear equations, obtained from such a reduction and defined on only 5 points of the lattice, will be shown to correspond to a coupling of a Tzitzeica equation to two linear equations. The Lax representation of this system is also presented.

Keywords

37K1035Q58
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 47 , Issue A , June 2005 , pp. 221 - 231
Copyright
2005 Glasgow Mathematical Journal Trust