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Generalized \((\frac{G^{\prime }}{G})\)-expansion method and exact traveling wave solutions of the perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity in optical fiber materials

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Abstract

In this paper, we investigate the nonlinear the perturbed nonlinear Schrödinger’s equation (NLSE) with Kerr law nonlinearity given in Zhang et al. (Appl Math Comput 216:3064–3072, 2010) and obtain new exact traveling solutions by using generalized \((\frac{G^{\prime }}{G})\)-expansion method. Under some parameter conditions, some explicit expressions of solutions for the equation are obtained. These solutions contain hyperbolic function solutions, trigonometric function solutions and rational function solution.

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Acknowledgements

This work was supported by Hunan Provincial Natural Science Foundation of China No.2016JJ2061, Scientific Research Fund of Hunan Provincial Education Department No.15B102, China Postdoctoral Science Foundation No.2013M532169, No.2014T70991, NNSF of China Grant No.11671101, the construct program of the key discipline in Hunan province No.201176 and and the Aid program for Science and Technology Innovative Research Team in Higher Educational Instituions of Hunan Province (No. 2014207), the Key Built Disciplines of Hunan University of Finance and Economics.

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  1. School of Mathematics, Hunan Institute of Science and Technology, Yueyang, 414006, Hunan Province, People’s Republic of China

    Zaiyun Zhang

  2. College of Science, National University of Defense Technology, Changsha, 410073, Hunan Province, People’s Republic of China

    Zaiyun Zhang

  3. Department of Basic Subjects, Hunan University of Finance and Economics, 139, 2nd Fenglin Road, Yuelu District, Changsha, 410205, Hunan Province, People’s Republic of China

    Jianguo Wu

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  1. Zaiyun Zhang
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Zhang, Z., Wu, J. Generalized \((\frac{G^{\prime }}{G})\)-expansion method and exact traveling wave solutions of the perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity in optical fiber materials. Opt Quant Electron 49, 52 (2017). https://doi.org/10.1007/s11082-016-0884-4

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