scholarly journals Spatial and temporal feedback control of traveling wave solutions of the two-dimensional complex Ginzburg–Landau equation

2007 ◽  
Vol 236 (1) ◽  
pp. 65-74 ◽  
Author(s):  
Claire M. Postlethwaite ◽  
Mary Silber
Keyword(s):  
Feedback Control ◽  
Traveling Wave ◽  
Landau Equation ◽  
Traveling Wave Solutions ◽  
Two Dimensional ◽  
Ginzburg Landau ◽  
Wave Solutions ◽  
Ginzburg Landau Equation

scholarly journals New Exact Traveling Wave Solutions of the Time Fractional Complex Ginzburg-Landau Equation via the Conformable Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhao Li ◽  
Tianyong Han
Keyword(s):  
Traveling Wave ◽  
Landau Equation ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Wave Transformation ◽  
Hyperbolic Function ◽  
Ginzburg Landau ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Ginzburg Landau Equation

In this study, the exact traveling wave solutions of the time fractional complex Ginzburg-Landau equation with the Kerr law and dual-power law nonlinearity are studied. The nonlinear fractional partial differential equations are converted to a nonlinear ordinary differential equation via a traveling wave transformation in the sense of conformable fractional derivatives. A range of solutions, which include hyperbolic function solutions, trigonometric function solutions, and rational function solutions, is derived by utilizing the new extended G ′ / G -expansion method. By selecting appropriate parameters of the solutions, numerical simulations are presented to explain further the propagation of optical pulses in optic fibers.

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