Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2012-01-05
Nonlinear Sciences
Exactly Solvable and Integrable Systems
14 pages, 4 figures, accepted by Commun. Nonlinear Sci. Numer. Simul
Scientific paper
10.1016/j.cnsns.2011.12.009
In this paper, we consider a general form of nonlinear Schr\"{o}dinger equation with time-dependent nonlinearity. Based on the linear eigenvalue problem, the complete integrability of such nonlinear Schr\"{o}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.
Ding Qi
Tian Shou-Fu
Zhang Hong-Qing
Zou Liuhua
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