Darboux Transformations of Integrable Couplings and Applications
Matrix spectral problem, integrable coupling, Darboux transformation, non-semisimple Lie algebra, soliton
Digital Object Identifier (DOI)
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
Scholar Commons Citation
Ma, Wen-Xiu and Zhang, Yu-Juan, "Darboux Transformations of Integrable Couplings and Applications" (2018). Mathematics and Statistics Faculty Publications. 100.