Title

Darboux Transformations of Integrable Couplings and Applications

Document Type

Article

Publication Date

2018

Keywords

Matrix spectral problem, integrable coupling, Darboux transformation, non-semisimple Lie algebra, soliton

Digital Object Identifier (DOI)

https://doi.org/10.1142/S0129055X18500034

Abstract

A formulation of Darboux transformations is proposed for integrable couplings, based on non-semisimple matrix Lie algebras. Applications to a kind of integrable couplings of the AKNS equations are made, along with an explicit formula for the associated Bäcklund transformation. Exact one-soliton-like solutions are computed for the integrable couplings of the second- and third-order AKNS equations, and a type of reduction is created to generate integrable couplings and their one-soliton-like solutions for the NLS and MKdV equations.

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Citation / Publisher Attribution

Reviews in Mathematical Physics, v. 30, issue 2, art. 1850003

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