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Novel Asymptotic Soliton Waves for the Nonlinear Schr¨odinger Equation with Varying Gain/Loss and Frequency Chirping

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Novel Asymptotic Soliton Waves for the Nonlinear Schr¨odinger Equation with Varying Gain/Loss and Frequency Chirping

Xian-Jing Laiaand Jie-Fang Zhangb

aDepartment of Basic Science, Zhejiang Shuren University, Hangzhou, 310015, Zhejiang, China

bInstitute of Theoretical Physics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China Reprint requests to X.-J. L.; E-mail: laixianjing@163.com

Z. Naturforsch.64a,347 – 353 (2009); received September 19, 2008 / revised February 22, 2009 This paper analysis spatial asymptotic waves propagation in nonuniform optical fiber. It finds an ap- propriate transformation such that the nonlinear variable-coefficient Schr¨odinger equation transform into the nonlinear Schr¨odinger equation with varying gain/loss and frequency chirping. It obtains solitonlike and periodic self-similar asymptotic waves by using the transformation. We analyze the evolution properties of some novel self-similar solutions. In addition, the nature of our self-similar asymptotic wave hints to the possibility of designing optical amplifier and focusing of spatial waves to overcome inevitable energy losses while performing in the optical nonlinear media.

Key words:Self-Similar Asymptotic Wave; Nonlinear Schr¨odinger Equation; Varying Gain/Loss;

Frequency Chirping.

PACS numbers:01.55.+b; 02.30.Jr

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