摘要
An integrable discrete system obtained by the algebraization of the difference operator is studied. The system is named discrete generalized nonlinear Schr¨odinger(GNLS) equation, which can be reduced to classical discrete nonlinear Schr¨odinger(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.
An integrable discrete system obtained by the algebraization of the difference operator is studied. The system is named discrete generalized nonlinear Schr¨odinger(GNLS) equation, which can be reduced to classical discrete nonlinear Schr¨odinger(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.
基金
Supported by the National Natural Science Foundation of China under Grant Nos.11375090,11275072
Innovative Research Team Program of the National Natural Science Foundation of China under Grant No.61021004
National High Technology Research and Development Program under No.2011AA010101
Shanghai Leading Academic Discipline Project under No.B412
