Breathers and multi-soliton solutions for the higher-order generalized nonlinear Schr?dinger equation

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• 作者：Rui Guo ; Hui-Qin Hao ; ^{gr81@sina.com}
• 关键词：The higher-order generalized nonlinear Schrö ; dinger equation ; Darboux transformation ; Breather ; Soliton solution ; Bound soliton
• 刊名：Communications in Nonlinear Science and Numerical Simulation
• 出版年：2013
• 出版时间：September, 2013
• 年：2013
• 卷：18
• 期：9
• 页码：2426-2435
• 全文大小：1978 K

文摘

In this paper, the higher-order generalized nonlinear Schr?dinger equation, which describes the propagation of ultrashort optical pulse in optical fibers, is analytically investigated. By virtue of the Darboux transformation constructed in this paper, some exact soliton solutions on the continuous wave (cw) background are generated. The following propagation characteristics of those solitons are mainly discussed: (1) Propagation of two types of breathers which delineate modulation instability and bright pulse propagation on a cw background respectively; (2) Two types propagation characteristics of two-solitons: elastic interactions and mutual attractions and repulsions bound solitons. Those results might be useful in the study of ultrashort optical solitons in optical fibers.