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Complex Ginzburg–Landau equation; complete discrimination system for polynomial method; trial equation method; exact travelling wave solutions

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 Jacobianelliptic 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.

YANG LIU^{1 2} SHUANGQING CHEN¹ LIXIN WEI^{1 2} BING GUAN¹

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

Published

1 August 2018

Manuscript received

13 November 2017

Manuscript revised

26 January 2018

Accepted

31 January 2018

Early published

Unedited version published online

Final version published online

17 July 2018