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.
Was this content written or created while at USF?
Yes
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.
https://digitalcommons.usf.edu/mth_facpub/100
