Stability analysis, optical solitons and complexitons of the two-dimensional complex Ginzburg-Landau equation

ABSTRACT

In this paper, the two-dimensional complex Ginzburg-Landau equation is investigated, which describes phase transitions in superconductors near their critical temperature in the field of electromagnetic behavior dynamics and in the study of external magnetic fields. We employ the hypothetical method to find the bright soliton, dark soliton and complexitons of the equation. We also find its power series solution with its convergence analysis. Moreover, some constraint conditions are provided which can guarantee the existence of solitons. By use of the Hamiltonian description, we analyze the modulation instability and stable solutions. In order to further understand the dynamic behavior, the graphics analysis is provided of these solutions.

Keywords:

• Two-dimensional complex Ginzburg-Landau equation
• bright soliton
• dark soliton
• stability analysis
• complexitons

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Jiangsu Province Natural Science Foundation of China [grant no. BK20181351], the Postgraduate Research & Practice Program of Education & Teaching Reform of CUMT [grant no. YJSJG_2018_036], the ‘Qinglan Engineering project’ of Jiangsu Universities, the National Natural Science Foundation of China [grant nos. 11301527 and 51522902], the No. [2016]22 supported by Ministry of Industry and Information Technology of China, the Fundamental Research Fund for the Central Universities [grant nos. 2017XKQY101 and DUT17ZD233], and the General Financial Grant from the China Postdoctoral Science Foundation [grant nos. 2015M570498 and 2017T100413].

Notes on contributors

Jin-Jin Mao

Jin-Jin Mao was born in Anhui, China, in 1992. She received the B.S. degree in Mathematics and Applied Mathematics from Information College of Huaibei Normal University, Huaibei, China, in 2017. She is currently working toward the Master degree in Computational Mathematics in China University of Mining and Technology, Xuzhou, China. Her main research interests include Integrable Systems and Their Applications and Soliton Theory.

Shou-Fu Tian

Shou-Fu Tian was born in Shandong, China, in 1984. He received the Ph.D. degree in applied mathematics from the Dalian University of Technology, in 2012. He is currently a Associate Professor, a Doctoral Supervisor, and the Associate Director of the Department of Mathematics and Applied Mathematics, China University of Mining and Technology. His main research interests include the fields of Nonlinear Mathematical Physics, Integrable Systems and Their Applications, Soliton Theory, etc.

Li Zou

Li Zou was born in Liaoning, China, in 1981. She received the Ph.D. degree in Design and Manufacture of Ships and Marine Structures from Dalian University of Technology, Dalian, China, in 2008. His main research interests include Design and Manufacture of Ships and Marine Structures. Integrable Systems and Their Applications, Soliton Theory.

Tian-Tian Zhang

Tian-Tian Zhang was born in Shandong, China, in 1986. She received the Master degree in computational mathematics from the Shanghai University, in 2011. She is currently a Lecturer, China University of Mining and Technology. She is currently working toward the Ph.D. degree in Applied Mathematics in China University of Mining and Technology, Xuzhou, China. Her main research interests include the fields of Nonlinear Mathematical Physics, Integrable Systems and Their Applications, Soliton Theory, etc.