Exact Traveling Wave Solutions for Higher Order Nonlinear Schrödinger Equations in Optics by Using the (G'/G, 1/G)-expansion Method

2015 ◽  
Vol 28 (4) ◽  
pp. 332-357 ◽  
Author(s):  
Zayed E. M. E.
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Higher Order ◽  
Nonlinear Schrödinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Nonlinear Schrodinger Equations

scholarly journals Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Zhao Li ◽  
Peng Li ◽  
Tianyong Han
Keyword(s):  
Traveling Wave ◽  
Variable Coefficients ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Nonlinear Schrodinger Equations ◽  
Coupled Nonlinear Schrodinger Equations

In this paper, the dynamical properties and the classification of single traveling wave solutions of the coupled nonlinear Schrödinger equations with variable coefficients are investigated by utilizing the bifurcation theory and the complete discrimination system method. Firstly, coupled nonlinear Schrödinger equations with variable coefficients are transformed into coupled nonlinear ordinary differential equations by the traveling wave transformations. Then, phase portraits of coupled nonlinear Schrödinger equations with variable coefficients are plotted by selecting the suitable parameters. Furthermore, the traveling wave solutions of coupled nonlinear Schrödinger equations with variable coefficients which correspond to phase orbits are easily obtained by applying the method of planar dynamical systems, which can help us to further understand the propagation of the coupled nonlinear Schrödinger equations with variable coefficients in nonlinear optics. Finally, the periodic wave solutions, implicit analytical solutions, hyperbolic function solutions, and Jacobian elliptic function solutions of the coupled nonlinear Schrödinger equations with variable coefficients are constructed.

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