Elliptic N-soliton Solutions of ABS Lattice Equations

Nijhoff, Frank and Atkinson, James (2010) Elliptic N-soliton Solutions of ABS Lattice Equations. International Mathematics Research Notices, 2010 (20). pp. 3837-3895. ISSN 1073-7928

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Official URL: http://dx.doi.org/10.1093/imrn/rnq010

Abstract

Elliptic N-soliton-type solutions, that is, solutions emerging from the application of N consecutive Bäcklund transformations to an elliptic seed solution, are constructed for all equations in the Adler-Bobenko-Suris (ABS) list of quadrilateral lattice equations, except for the case of the Q4 equation which is treated elsewhere. The main construction, which is based on an elliptic Cauchy matrix, is performed for the equation Q3, and by coalescence on certain auxiliary parameters, the corresponding solutions of the remaining equations in the list are obtained. Furthermore, the underlying linear structure of the equations is exhibited, leading, in particular, to a novel Lax representation of the Q3 equation.

Item Type: Article
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Ay Okpokam
Date Deposited: 06 Nov 2013 10:13
Last Modified: 10 Aug 2015 11:24
URI: http://nrl.northumbria.ac.uk/id/eprint/14480

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