Abstract
In this paper, Bose–Einstein soliton solutions of the nonlinear Schrödinger equation with time-dependent linear potential are considered. Based on the F-expansion method, we present a number of Jacobian elliptic function solutions. Particular cases of these solutions, where the elliptic function modulus equals 1 and 0, are various localized solutions and trigonometric functions, respectively. Specially, for V ext = ZF( T) = Z[ mg + Hcos ( ω 1 T)], we discussed the Bose–Einstein condensate trapped in the coupling external field with considering the effect of gravity; for F( T) = constant, it describes the wave (Langmuir or electromagnetic) in a linearly inhomogeneous plasma with cubic nonlinearly.
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