A Generalized Method and Exact Solutions in Bose-Einstein Condensates in an Expulsive Parabolic Potential |
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Authors: | LI Biao CHEN Yong |
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Institution: | 1. Nonlinear Science Center and Department of Mathematics,
Ningbo University, Ningbo 315211, China
;2. Institute of Theoretical Computing, East China Normal
University, Shanghai 200062, China
;3. MM Key Lab, the Chinese Academy of Sciences, Beijing 100080, China |
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Abstract: | In the paper, a generalized sub-equation method is presented to construct some exact analytical solutions of nonlinear partial differential equations. Making use of the method, we present rich exact analytical solutions of the one-dimensional nonlinear Schrödinger equation which describes the dynamics of solitons in Bose-Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic potential. The solutions obtained include not only non-traveling wave and coefficient function's
soliton solutions, but also Jacobi elliptic function solutions and
Weierstrass elliptic function solutions. Some plots are given to
demonstrate the properties of some exact solutions under the
Feshbach-managed nonlinear coefficient and the hyperbolic secant function coefficient. |
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Keywords: | nonlinear Schrodinger equation symbolic computation soliton |
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