High-order rogue waves and their dynamics of the Fokas-Lenells equation revisited: a variable separation technique

The Fokas-Lenells (FL) equation is an integrable higher-order extension of nonlinear Schrodinger 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.