Characteristics of the breather and rogue waves in a (2+1)-dimensional nonlinear Schrödinger equation
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- by Xiu-Bin Wang, Shou-Fu Tian and Tian-Tian Zhang PDF
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Abstract:
Under investigation in this paper is a (2+1)-dimensional nonlinear Schrödinger equation (NLS), which is a generalisation of the NLS equation. By virtue of Wronskian determinants, an effective method is presented to succinctly construct the breather wave and rogue wave solutions of the equation. Furthermore, the main characteristics of the breather and rogue waves are graphically discussed. The results show that rogue waves can come from the extreme behavior of the breather waves. It is hoped that our results could be useful for enriching and explaining some related nonlinear phenomena.References
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Additional Information
- Xiu-Bin Wang
- Affiliation: School of Mathematics and Institute of Mathematical Physics, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China
- MR Author ID: 1156525
- Email: wangxiubin123@cumt.edu.cn
- Shou-Fu Tian
- Affiliation: School of Mathematics and Institute of Mathematical Physics, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China – and – Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
- Address at time of publication: School of Mathematics and Institute of Mathematical Physics, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China
- MR Author ID: 894745
- Email: sftian@cumt.edu.cn, shoufu2006@126.com
- Tian-Tian Zhang
- Affiliation: School of Mathematics and Institute of Mathematical Physics, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China
- MR Author ID: 907456
- Email: ttzhang@cumt.edu.cn
- Received by editor(s): February 20, 2017
- Received by editor(s) in revised form: March 12, 2017, and March 30, 2017
- Published electronically: April 17, 2018
- Additional Notes: This work was supported by the Fundamental Research Fund for the Central Universities under the Grant No. 2017XKQY101.
Shou-Fu Tian served as corresponding author for this paper. - Communicated by: Mourad Ismail
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 3353-3365
- MSC (2010): Primary 35Q55, 35Q51; Secondary 35P30, 81Q05
- DOI: https://doi.org/10.1090/proc/13765
- MathSciNet review: 3803661