Generalized $$(\frac{G^{\prime }}{G})$$ ( G ′ G ) -expansion method and exact traveling wave solutions of the perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity in optical fiber materials

2017 ◽  
Vol 49 (2) ◽  
Author(s):  
Zaiyun Zhang ◽  
Jianguo Wu
Keyword(s):  
Optical Fiber ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Kerr Law ◽  
Kerr Law Nonlinearity ◽  
Fiber Materials ◽  
Schrödinger's 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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