High-order rogue waves and their dynamics of the Fokas–Lenells equation revisited: a variable separation technique
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The Fokas–Lenells (FL) equation is an integrable higher-order extension of nonlinear Schrödinger equation. One approach to generating its breather solutions is based on Darboux transformation (DT) and iterations. However, the DT of FL equation contains negative powers of the spectral parameter, which can lead to very complicated expressions when N is large. In this paper, we avoid the negative powers by adopting a variable separation and Taylor expansion technique to solve the Lax pair of FL system. Furthermore, stability of the proposed technique is demonstrated in detail.
KeywordsFokas–Lenells equation Lax pairs Variable separation Rogue waves
This work is sponsored by the National Natural Science Foundation of China (No. 11571079, No. 11801153, No. 11701322), Shanghai Pujiang Program (No. 14PJD007), the Natural Science Foundation of Shanghai (No. 14ZR1403500) and the Young Teachers Foundation (No. 1411018) of Fudan University. Also, the authors are very grateful to Professor Peter D. Miller and Professor John E. Fornaess for their enthusiastic support and useful suggestions.
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Conflict of interest
The authors declare that there is no conflict of interest.