An Integrable Discrete Generalized Nonlinear Schrodinger Equation and Its Reductions

摘要

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.