General rogue wave solutions of the coupled Fokas-Lenells equations and non-recursive Darboux transformation

Year: 2019

Authors: Ye YL., Zhou Y., Chen SH., Baronio F., Grelu P.

Autors Affiliation: Southeast Univ, Sch Phys, Nanjing 211189, Jiangsu, Peoples R China; CNR, INO, Via Branze 38, I-25123 Brescia, Italy; Univ Brescia, Dipartimento Ingn Informaz, Via Branze 38, I-25123 Brescia, Italy; Univ Bourgogne Franche Comte, CNRS, Lab ICB, UMR 6303, 9 Ave A Savary, F-21078 Dijon, France.

Abstract: We formulate a non-recursive Darboux transformation technique to obtain the general nth-order rational rogue wave solutions to the coupled Fokas-Lenells system, which is an integrable extension of the noted Manakov system, by considering both the double-root and triple-root situations of the spectral characteristic equation. Based on the explicit fundamental and second-order rogue wave solutions, we demonstrate several interesting rogue wave dynamics, among which are coexisting rogue waves and anomalous Peregrine solitons. Our solutions are generalized to include the complete background-field parameters and therefore helpful for future experimental study.

Journal/Review: PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCE

Volume: 475 (2224)      Pages from: 20180806-1  to: 20180806-18

More Information: This work was supported by the National Natural Science Foundation of China (grant no. 11474051) and by the Scientific Research Foundation of Graduate School of Southeast University (grant no. YBPY1872). F.B. was supported by the European Union?s Horizon 2020 research and innovation program MSCA-RISE-2015 (grant no. 691051). P.G. was supported by CEFIPRA under contract 5104-2.
KeyWords: rogue waves; Peregrine solitons; Fokas-Lenells equation; Darboux transformation
DOI: 10.1098/rspa.2018.0806

Citations: 34
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