arXiv subjects

Dingbian Qian

Publications and source records attributed to Dingbian Qian.

2 recordsLinked to original sources

arXiv2011

Modulated amplitude waves with nonzero phases in Bose-Einstein condensates

In this paper we give a frame for application of the averaging method to Bose-Einstein condensates (BECs) and obtain an abstract result upon the dynamics of BECs. Using aver- aging method, we determine the location where the modulated amplitude waves (periodic or quasi-periodic) exist and we also study the stability and instability of modulated amplitude waves (periodic or quasi-periodic). Compared with the previous work, modulated amplitude waves studied in this paper have nontrivial phases and this makes the problem become more diffcult, since it involves some singularities.

nlin.CD↗

arXiv2011

Construction of modulated amplitude waves via averaging in collisionally inhomogeneous Bose-Einstein condensates

We apply the averaging method to analyze spatio-temportal structures in nonlinear Schrödinger equations and thereby study the dynamics of quasi-one-dimensional collisionally inhomogeneous Bose-Einstein condensates with the scattering length varying periodically in spatial and crossing zero. Infinitely many (positive measure set) modulated amplitude waves (periodic and quasi-periodic), which are instable, can be proved to exist by adjusting the intergration constant c on some open interval. Finally, some numerical simulations support our results.

nlin.PS↗