Generalized Darboux Transformations, Rogue Waves, and Modulation Instability for the Coherently Coupled Nonlinear Schrödinger Equations in Nonlinear Optics

2019 ◽  
Vol 531 (8) ◽  
pp. 1900011 ◽  
Author(s):  
Su-Su Chen ◽  
Bo Tian ◽  
Yan Sun ◽  
Chen-Rong Zhang
Keyword(s):  
Nonlinear Optics ◽  
Modulation Instability ◽  
Rogue Waves ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Darboux Transformations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

Mixed interaction solutions for the coupled nonlinear Schrödinger equations

2021 ◽  
pp. 2150004
Author(s):  
Yaning Tang ◽  
Jiale Zhou
Keyword(s):  
Darboux Transformation ◽  
Rogue Waves ◽  
Transformation Method ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Interaction Solutions ◽  
Nonlinear Schrodinger Equations

We investigate the mixed interaction solutions of the coupled nonlinear Schrödinger equations (CNLSE) through the Darboux transformation method. First of all, we derive the nonsingular localized wave solutions for two cases of CNLSE by the Darboux transformation method and matrix analysis method. Furthermore, we take a limit technique to deduce rogue waves and divide the rogue waves into four categories through analyzing their dynamic behaviors. Based on the obtained theorems, the Darboux transformations are presented to solve interaction solutions between distinct nonlinear waves. In this paper, we mainly study four types. Finally, the dynamic characteristics of the constructed these solutions are analyzed by sequences of interesting figures plotted with the help of Maple.

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