Engineering integrable nonautonomous nonlinear Schroedinger equations
- School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000 (China)
- Department of Modern Physics, Lanzhou University, Lanzhou 73000 (China)
- Center for Interdisciplinary Studies, Lanzhou University, Lanzhou 730000 (China)
We investigate Painleve integrability of a generalized nonautonomous one-dimensional nonlinear Schroedinger (NLS) equation with time- and space-dependent dispersion, nonlinearity, and external potentials. Through the Painleve analysis some explicit requirements on the dispersion, nonlinearity, dissipation/gain, and the external potential as well as the constraint conditions are identified. It provides an explicit way to engineer integrable nonautonomous NLS equations at least in the sense of Painleve integrability. Furthermore analytical solutions of this class of integrable nonautonomous NLS equations can be obtained explicitly from the solutions of the standard NLS equation by a general transformation. The result provides a significant way to control coherently the soliton dynamics in the corresponding nonlinear systems, as that in Bose-Einstein condensate experiments. We analyze explicitly the soliton dynamics under the nonlinearity management and the external potentials and discuss its application in the matter-wave dynamics. Some comparisons with the previous works have also been discussed.
- OSTI ID:
- 21294127
- Journal Information:
- Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 79, Issue 5; Other Information: DOI: 10.1103/PhysRevE.79.056610; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1539-3755
- Country of Publication:
- United States
- Language:
- English
Similar Records
On the Nonautonomous Nonlinear Schroedinger Equations and Soliton Management
Multi-soliton management by the integrable nonautonomous nonlinear integro-differential Schrödinger equation