Darboux and binary Darboux transformations for discrete integrable systems 1. Discrete potential KdV equation
arXiv:1309.5512 · doi:10.1088/1751-8113/47/2/025205
Abstract
The Hirota-Miwa equation can be written in `nonlinear' form in two ways: the discrete KP equation and, by using a compatible continuous variable, the discrete potential KP equation. For both systems, we consider the Darboux and binary Darboux transformations, expressed in terms of the continuous variable, and obtain exact solutions in Wronskian and Grammian form. We discuss reductions of both systems to the discrete KdV and discrete potential KdV equations, respectively, and exploit this connection to find the Darboux and binary Darboux transformations and exact solutions of these equations.
References in corpus (7)
- Classification of integrable equations on quad-graphs. The consistency approach
- Soliton Solutions for ABS Lattice Equations: I Cauchy Matrix Approach
- Soliton Solutions for ABS Lattice Equations II: Casoratians and Bilinearization
- A survey of Hirota's difference equations
- Quasideterminant solutions of a non-Abelian Hirota-Miwa equation
- An Inverse Scattering Transform for the Lattice Potential KdV Equation
- Bilinearization and Casorati determinant solution to the non-autonomous discrete KdV equation