Exact Solutions of Bose-Einstein Condensate in Linear Magnetic Field and Time-Dependent Laser Field

Abstract

Nonlinear evolution equations (NLEEs) are frequently used to model a wide variety of phenomena in physics, chemistry, biology and even in social science field. Seeking and constructing exact solutions especially soliton solutions of NLEEs is one of the most important and essential task in nonlinear science. With the help of exact solutions, when they exist, the nonlinear phenomena can be better understood. In the past decades, various sophisticated methods have been created such as the inverse scattering method [1], the Backlund transformations [2], the Darboux transformations [3] and the Hirota bilinear method [4]. Especially, in recent years, with the rapid development of computerized symbolic computation, many direct and effective algebraic methods are proposed such as the homogeneous balance method [5], tanh function method [6], the Jacobi elliptic function expansion method [7], the F-expansion techniques [8], exp-function method [9] and so on. Recently, Wang et al. [10] introduced a new direct method called G ′ G -expansion method for a reliable treatment of the NLEEs. Then this method is generalized and widely used to seek travelling wave solutions, non-travelling wave solutions and coefficient function solutions for many nonlinear physical models [11–14], and even extended to solve NLEE with variable coefficients [15]. The Gross–Pitaevskii equation appears as a relevant model in various areas of physics: nonlinear optics, fluid mechanics, Bose–Einstein condensation (BEC). The realization of BEC of weakly interacting atomic gases stim-