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Exact solutions to complex Ginzburg–Landau equation

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Abstract

In this paper, the trial equation method and the complete discrimination system for polynomial method are applied to retrieve the exact travelling wave solutions of complex Ginzburg–Landau equation. Both the Kerr and power laws of nonlinearity are considered. All the possible exact travelling wave solutions consisting of the rational function-type solutions, solitary wave solutions, triangle function-type periodic solutions and Jacobian elliptic functions solutions are obtained, and some of them are new solutions. In addition, concrete examples are presented to ensure the existence of obtained solutions. Moreover, four types of representative solutions are depicted to present the nature of the obtained solutions.

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Acknowledgements

This study was supported by National Natural Science Foundation of China (Grant No. 51674086); the Northeast Petroleum University Innovation Foundation for Postgraduate (Grant No. YJSCX2015-012NEPU).

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Authors and Affiliations

  1. School of Petroleum Engineering, Northeast Petroleum University, Daqing, China

    Yang Liu, Shuangqing Chen, Lixin Wei & Bing Guan

  2. Key Laboratory of Oil and Gas Storage and Transportation of CNPC, Northeast Petroleum University, Daqing, China

    Yang Liu & Lixin Wei

Authors
  1. Yang Liu
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  2. Shuangqing Chen
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  3. Lixin Wei
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  4. Bing Guan
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Correspondence to Shuangqing Chen.

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Liu, Y., Chen, S., Wei, L. et al. Exact solutions to complex Ginzburg–Landau equation. Pramana - J Phys 91, 29 (2018). https://doi.org/10.1007/s12043-018-1603-4

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  • DOI: https://doi.org/10.1007/s12043-018-1603-4

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