Generalized Darboux transformation and nonlinear analysis of higher-order localized wave solutions

Localized Waves for the Coupled Mixed Derivative Nonlinear Schrödinger Equation in a Birefringent Optical Fiber

“…Further, These nonlinear equations can be used to describe and study localized waves, which consist of rogue waves [10,11], solitons [12,13], and breathers [14][15][16][17]. To date, some methods have been proposed and applied to investigate localized waves of coupled systems, such as the Darboux transformation (DT) [18], the Riemann-Hilbert approach [19], the Hirota bilinear method [20], the generalized DT [21], and so on. Due to the profound theoretical significance and potential applicability, the study of localized waves of the nonlinear PDEs has always been concerned, and great progress has been made [22][23][24][25][26][27][28][29].…”