Conservation laws, bright matter wave solitons and modulational instability of nonlinear Schr枚dinger equation with time-dependent nonlinearity

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• 作者：Shou-Fu Tian^a ; ^b ; ^{shoufu2006@126.com} ; ^{shoufu@math.ubc.ca} ; Li Zou^c ; Qi Ding^a ; Hong-Qing Zhang^a
• 关键词：Exact solution ; Bright matter wave soliton ; Conservation law ; Modulational instability ; Nonlinear Schrö ; dinger equation with time-dependent nonlinearity
• 刊名：Communications in Nonlinear Science and Numerical Simulation
• 出版年：2012
• 期刊代码：89_10075704
• 类别：ph
• 出版时间：August, 2012
• 卷：17
• 期：8
• 页码：3247-3257
• 文件大小：1141 K

摘要

In this paper, we consider a general form of nonlinear Schr枚dinger equation with time-dependent nonlinearity. Based on the linear eigenvalue problem, the complete integrability of such nonlinear Schr枚dinger equation is identified by admitting an infinite number of conservation laws. Using the Darboux transformation method, we obtain some explicit bright multi-soliton solutions in a recursive manner. The propagation characteristic of solitons and their interactions under the periodic plane wave background are discussed. Finally, the modulational instability of solutions is analyzed in the presence of small perturbation.