A Constructive Approach to the Soliton Solutions of Integrable Quadrilateral Lattice Equations

Atkinson, James and Nijhoff, Frank (2010) A Constructive Approach to the Soliton Solutions of Integrable Quadrilateral Lattice Equations. Communications in Mathematical Physics, 299 (2). pp. 283-304. ISSN 0010-3616

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Official URL: http://dx.doi.org/10.1007/s00220-010-1076-x

Abstract

Scalar multidimensionally consistent quadrilateral lattice equations are studied. We explore a confluence between the superposition principle for solutions related by the Bäcklund transformation, and the method of solving a Riccati map by exploiting two known particular solutions. This leads to an expression for the N-soliton-type solutions of a generic equation within this class. As a particular instance we give an explicit N-soliton solution for the primary model, which is Adler’s lattice equation (or Q4).

Item Type: Article
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics and Information Sciences
Depositing User: Becky Skoyles
Date Deposited: 02 Oct 2013 10:01
Last Modified: 10 Aug 2015 11:23
URI: http://nrl.northumbria.ac.uk/id/eprint/13628

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