|
Z. Naturforsch. 66a, 728 – 734
(2011)
doi:10.5560/ZNA.2011-0043
Localized Nonlinear Waves in Nonlinear Schrödinger Equation with Nonlinearities Modulated in Space and Time
Department of Mathematics, Ningbo University Ningbo 315211, P. R. China
Received April 29, 2011
Reprint requests to: B. L.; E-mail:
biaolee2000@yahoo.com.cn
In this paper, the generalized sub-equation method is extended to investigate localized nonlinear waves of the one-dimensional nonlinear Schrödinger equation (NLSE) with potentials and nonlinearities depending on time and on spatial coordinates. With the help of symbolic computation, three families of analytical solutions of this NLS-type equation are presented. Based on these solutions, periodically and quasiperiodically oscillating solitons (dark and bright) and moving solitons are observed. Some implications to Bose–Einstein condensates are also discussed.
Key words: Nonlinear Schrödinger Equation; Time- and Space-Modulated Nonlinearities; Solitons; Bose–Einstein Condensates.