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Discrete Dynamics in Nature and Society
Volume 2016 (2016), Article ID 7879517, 9 pages
Research Article

Rogue Waves of Nonlinear Schrödinger Equation with Time-Dependent Linear Potential Function

Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China

Received 23 November 2015; Accepted 24 January 2016

Academic Editor: Amit Chakraborty

Copyright © 2016 Ni Song and Yakui Xue. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The rogue waves of the nonlinear Schrödinger equation with time-dependent linear potential function are investigated by using the similarity transformation in this paper. The first-order and second-order rogue waves solutions are obtained and the nonlinear dynamic behaviors of these solutions are discussed in detail. In addition, the amplitudes of the rogue waves under the effect of the gravity field and external magnetic field changing with the time are analyzed by using numerical simulation. The results can be used to study the matter rogue waves in the Bose-Einstein condensates and other fields of nonlinear science.