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THE BOUSSINESQ INTEGRABLE SYSTEM: COMPATIBLE LATTICE AND CONTINUUM STRUCTURES

Published online by Cambridge University Press:  14 July 2005

ANASTASIOS TONGAS  and
FRANK NIJHOFF
ANASTASIOS TONGAS
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, U.K.
FRANK NIJHOFF
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, U.K.
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Abstract

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We consider the discrete Boussinesq integrable system and the compatible set of differential difference, and partial differential equations. The latter not only encode the complete hierarchy of the Boussinesq equation, but also incorporate the hyperbolic Ernst equations for an Einstein-Maxwell-Weyl field in general relativity. We demonstrate a specific symmetry reduction of the partial differential equations, to a six-parameter, second order coupled system of ordinary differential equations, which is conjectured to be of Garnier type.

Keywords

35Q58
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 47 , Issue A , June 2005 , pp. 205 - 219
Copyright
2005 Glasgow Mathematical Journal Trust