Abstract
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 extendedG′/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.
Highlights
The Ginzburg-Landau (GL) equation [1,2,3,4,5,6,7] is one of the most important partial differential equations in the field of mathematics and physics, which was introduced into the study of superconductivity phenomenology theory in the 20th century by Ginzburg and Landau
Constructing the exact traveling solutions of the fractional GL equation is very important work because it can be better explained the dynamics of soliton propagation through optical fibers over longer distances in nonlinear optics
The time fractional complex GL equation with the Kerr law and dual-power law nonlinearity, which depicts the dynamics of soliton propagation through optical fibers over longer distances, is studied by using the extended ðG′/GÞ-expansion method
Summary
The Ginzburg-Landau (GL) equation [1,2,3,4,5,6,7] is one of the most important partial differential equations in the field of mathematics and physics, which was introduced into the study of superconductivity phenomenology theory in the 20th century by Ginzburg and Landau. Constructing the exact traveling solutions of the fractional GL equation is very important work because it can be better explained the dynamics of soliton propagation through optical fibers over longer distances in nonlinear optics. The main purpose of this paper is to construct exact traveling wave solutions of the time fractional complex GL equation with the Kerr law and dual-power law nonlinearity by using the new extended ðG′/GÞ-expansion method, and a range of solutions which include hyperbolic function solutions, trigonometric function solutions, rational function solutions, and negative power solutions is derived.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
