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

Chvartatskyi, Oleksandr; Dimakis, Aristophanes; Müller-Hoissen, Folkert

doi:10.1007/s11005-016-0859-1

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

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Chvartatskyi, Oleksandr
Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Müller-Hoissen, Folkert
Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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http://link.springer.com/article/10.1007%2Fs11005-016-0859-1
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Citation

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.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002B-18D7-7

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.