title: Traveling and solitary wave solutions to the one-dimensional Gross-Pitaevskii equation.
abstract: The evolution of traveling and solitary waves in Bose-Einstein condensates (BECs) with a time-dependent scattering length in an attractive/repulsive parabolic potential is studied. The homogeneous balance principle and the F-expansion technique are used to solve the one-dimensional Gross-Pitaevskii equation with time-varying coefficients. We obtained three classes of new exact traveling wave and localized solutions. Our results demonstrate that the BEC solitary wave solutions can be manipulated and controlled by the time-dependent scattering length.
authors.affiliation: Department of Electronic Engineering, Shunde Polytechnic, Guangdong Province, Shunde, China. zhongwp6@126.com
authors.forename: Wei-Ping
authors.initials: WP
authors.lastname: Zhong
authors.forename: Milivoj R
authors.initials: MR
authors.lastname: Belić
authors.forename: Yiqin
authors.initials: Y
authors.lastname: Lu
authors.forename: Tingwen
authors.initials: T
authors.lastname: Huang