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  Self-consistent sources for integrable equations via deformations of binary Darboux transformations.

Chvartatskyi, O., Dimakis, A., & Müller-Hoissen, F. (2016). Self-consistent sources for integrable equations via deformations of binary Darboux transformations. Letters in Mathematical Physics, 106(8), 1139-1179. doi:10.1007/s11005-016-0859-1.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002B-18D7-7 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002D-3D60-4
Genre: Journal Article

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 Creators:
Chvartatskyi, Oleksandr1, Author              
Dimakis, Aristophanes, Author
Müller-Hoissen, Folkert1, Author              
Affiliations:
1Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063285              

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Free keywords: Bidifferential calculus; Darboux transformation; Integrable systems; Self-consistent sources; KP; Discrete KP; Nonlinear Schrödinger; Davey-Stewartson; Toda lattice; Yajima-Oikawa
 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 KdV, Boussinesq, sine-Gordon, nonlinear Schrödinger, KP, Davey-Stewartson, two-dimensional Toda lattice and discrete KP equation. 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.

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Language(s): eng - English
 Dates: 2016-06-012016-08
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: Peer
 Identifiers: DOI: 10.1007/s11005-016-0859-1
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Title: Letters in Mathematical Physics
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: -
Pages: - Volume / Issue: 106 (8) Sequence Number: - Start / End Page: 1139 - 1179 Identifier: -