Soliton Solutions for ABS Lattice Equations: I Cauchy Matrix Approach

Details Soliton Solutions for ABS Lattice Equations: I Cauchy Matrix Approach Soliton Solutions for ABS Lattice Equations: I Cauchy Matrix Approach

2009-02-27

arxiv.org/abs/0902.4873v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

40 pages, 3 figures, submitted to Journal of Physics A: Mathematical and Theoretical, Special issue on nonlinearity and geomet

Scientific paper

In recent years there have been new insights into the integrability of quadrilateral lattice equations, i.e. partial difference equations which are the natural discrete analogues of integrable partial differential equations in 1+1 dimensions. In the scalar (i.e. single-field) case there now exist classification results by Adler, Bobenko and Suris (ABS) leading to some new examples in addition to the lattice equations "of KdV type" that were known since the late 1970s and early 1980s. In this paper we review the construction of soliton solutions for the KdV type lattice equations and use those results to construct N-soliton solutions for all lattice equations in the ABS list except for the elliptic case of Q4, which is left to a separate treatment.

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