Soliton Solutions for ABS Lattice Equations: I Cauchy Matrix Approach
نویسندگان
چکیده
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.
منابع مشابه
Soliton Solutions for ABS Lattice Equations: II: Casoratians and Bilinearization
In Part I soliton solutions to the ABS list of multi-dimensionally consistent difference equations (except Q4) were derived using connection between the Q3 equation and the NQC equations, and then by reductions. In that work central role was played by a Cauchy matrix. In this work we use a different approach, we derive the N -soliton solutions following Hirota’s direct and constructive method. ...
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