EXACT SOLUTIONS OF COUPLED KdV EQUATION DERIVED FROM THE COUPLED NLS EQUATION USING MULTIPLE SCALES METHOD

2011 ◽  
Vol 25 (29) ◽  
pp. 4021-4028
Author(s):  
FILIZ TAŞCAN ◽  
AHMET BEKIR
Keyword(s):  
Exact Solutions ◽  
Multiple Scales ◽  
Kdv Equation ◽  
Higher Order ◽  
Multiple Scales Method ◽  
Nonlinear Schrödinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Coupled Kdv Equation

In this paper, we have considered a generalized coupled higher-order nonlinear Schrödinger equations. We applied multiple scales method to coupled higher-order nonlinear Schrödinger equations to derive the coupled KdV equation. Then, the extended tanh method is applied to derived coupled KdV equation for exact solutions. The obtained results include solitary wave solutions.

scholarly journals N-Fold Darboux Transformation for the Classical Three-Component Nonlinear Schrödinger Equations and Its Exact Solutions

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 733
Author(s):  
Yu-Shan Bai ◽  
Peng-Xiang Su ◽  
Wen-Xiu Ma
Keyword(s):  
Exact Solutions ◽  
Gauge Transformation ◽  
Darboux Transformation ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Lax Pairs ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
The Given

In this paper, by using the gauge transformation and the Lax pairs, the N-fold Darboux transformation (DT) of the classical three-component nonlinear Schrödinger (NLS) equations is given. In addition, by taking seed solutions and using the DT, exact solutions for the given NLS equations are constructed.

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