An Integrable Discrete Generalized Nonlinear Schrödinger Equation and Its Reductions

An integrable discrete system obtained by the algebraization of the difference operator is studied. The system is named discrete generalized nonlinear Schrodinger (GNLS) equation, which can be reduced to classical discrete nonlinear Schrodinger (NLS) equation. Furthermore, all of the linear reductio...

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Bibliographic Details
Published inCommunications in theoretical physics Vol. 62; no. 5; pp. 641 - 648
Main Authors Li, Hong-Min, Li, Yu-Qi, Chen, Yong
Format Journal Article
LanguageEnglish
Published 01.11.2014
Subjects
Discrete systems
Mathematical analysis
Nonlinearity
Operators
Recursion
Reduction
Schroedinger equation
Symmetry
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Summary:An integrable discrete system obtained by the algebraization of the difference operator is studied. The system is named discrete generalized nonlinear Schrodinger (GNLS) equation, which can be reduced to classical discrete nonlinear Schrodinger (NLS) equation. Furthermore, all of the linear reductions for the discrete GNLS equation are given through the theory of circulant matrices and the discrete NLS equation is obtained by one of the reductions. At the same time, the recursion operator and symmetries of continuous GNLS equation are successfully recovered by its corresponding discrete ones.
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ISSN:0253-6102
1572-9494
DOI:10.1088/0253-6102/62/5/02