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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


A Method for Generating Lie Algebras and Applications

Discontinuity, Nonlinearity, and Complexity 1(3) (2012) 211--224 | DOI:10.5890/DNC.2012.05.004

Yufeng Zhang

College of Sciences, China University of Mining and Technology, Xuzhou 221116, P. R. China

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A way for generating Lie algebras from a Lie subalgebra of the Lie algebra A1 is proposed for which a few enlarged Lie algebras are constructed. By establishing their loop algebras and introducing Lax pairs, we obtain two integrable Hamiltonian hierarchies of evolution type, one of them reduces to the well-known nonlinear Schr¨odinger equation, another is a nonlinear integrable coupling of the Kaup-Newell (KN) hierarchy,which reduces to a coupled nonlinear integrable model with Hamiltonian structure.


This work was supported by Natural Science Foundatrion of Liaoning Province (grant number: 20092173).


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