Nonautonomous matter waves in a waveguide

Abstract

We present a physical model that describes the transport of Bose-Einstein-condensed atoms from a reservoir to a waveguide. By using the similarity and M\"obius transformations, we study nonautonomous matter waves in Bose-Einstein condensates in the presence of an inhomogeneous source. Then, we find its various types of exact nonautonomous matter-wave solutions, including the W-shaped bright solitary waves, W-shaped and U-shaped dark solitary waves, periodic wave solutions, and rational solitary waves. The results show that these different types of matter-wave structures can be generated and effectively controlled by modulating the amplitude of the source. Our results may raise the possibility of some experiments and potential applications related to Bose-Einstein condensates in the presence of an inhomogeneous source.