Collective Excitations and Nonlinear Dynamics of 1D BEC with Two- and Three-body Interactions in Anharmonic Traps

The collective excitations of low-dimensional Bose–Einstein condensates with two- and three-body interactions in anharmonic potentials are investigated. Using the standard variational approach, the governing equations of motions for the low-energy excitations are obtained by solving time-dependent Gross–Pitaevskii–Ginzburg equation, and the excitation spectrums are calculated in small amplitude limit. The frequency shift and nonlinear mode coupling induced by the anharmonic distortion (adding cubic, quartic, or quintic term to a harmonic trap) are studied.