Self-Consistent Sources for Integrable Equations via Deformations of Binary Darboux Transformations
Abstract
We reveal the origin and structure of self-consistent source extensions of integrable equations from the perspective of binary Darboux transformations. They arise via a deformation of the potential that is central in this method. As examples, we obtain in particular matrix versions of self-consistent source extensions of the sine-Gordon, nonlinear Schrodinger, KdV, Boussinesq, KP, Davey-Stewartson, two-dimensional Toda lattice and discrete KP systems. We also recover a (2+1)-dimensional version of the Yajima-Oikawa system from a deformation of the pKP hierarchy. By construction, these systems are accompanied by a hetero binary Darboux transformation, which generates solutions of such a system from a solution of the source-free system and additionally solutions of an associated linear system and its adjoint. The essence of all this is encoded in universal equations in the framework of bidifferential calculus.
Cite
@article{arxiv.1510.05166,
title = {Self-Consistent Sources for Integrable Equations via Deformations of Binary Darboux Transformations},
author = {Oleksandr Chvartatskyi and Aristophanes Dimakis and Folkert Müller-Hoissen},
journal= {arXiv preprint arXiv:1510.05166},
year = {2016}
}
Comments
35 pages, 1 figure, second version: some amendments, additional references, section 5 added