Envelope self-similar solutions for the nonautonomous and inhomogeneous nonlinear Schrödinger equation |
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Authors: | Chaoqing Dai Shiqun Zhu Jiefang Zhang |
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Affiliation: | a School of Physical Science and Technology, Suzhou University, Suzhou, Jiangsu, 215006, PR China b School of Sciences, Zhejiang Agriculture and Forestry University, Lin'an, Zhejiang, 311300, PR China c Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, PR China |
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Abstract: | By means of the similarity transformation connecting with the solvable stationary equation, the self-similar combined Jacobian elliptic function solutions and fractional form solutions of the generalized nonlinear Schrödinger equation (NLSE) are obtained when the dispersion, nonlinearity, and gain or absorption are varied. The propagation dynamics in a periodic distributed amplification system is investigated. Self-similar cnoidal waves and corresponding localized waves including bright and dark similaritons (or solitons) for NLSE and arch and kink similaritons (or solitons) for cubic-quintic NLSE are analyzed. The results show that the intensity and the width of chirped cnoidal waves (or similaritons) change more distinctly than that of chirp-free counterparts (or solitons). |
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Keywords: | Self-similar solutions Nonlinear Schrö dinger equation |
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