Darboux transformations of integrable couplings and applications
REVIEWS IN MATHEMATICAL PHYSICS(2018)
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 Backlund 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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Key words
Matrix spectral problem,integrable coupling,Darboux transformation,non-semisimple Lie algebra,soliton
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