This paper employs a novel $\varphi ^{6}$model expansion approach to get dark, bright, periodic, darkbright, and singular soliton solutions to the complex GinzburgLandau equation with dual powerlaw nonlinearity. The dualpower law found in photovoltaic materials is used to explain nonlinearity in the refractive index. The results of this paper may assist in comprehending some of the physical effects of various nonlinear physics models. For example, the hyperbolic sine arises in the calculation of the Roche limit and the gravitational potential of a cylinder, the hyperbolic tangent arises in the calculation of the magnetic moment and the rapidity of special relativity, and the hyperbolic cotangent arises in the Langevin function for magnetic polarization. Frequency values, one of the soliton's internal dynamics, are used to examine the behavior of the traveling wave. Finally, some of the obtained solitons' three, twodimensional, and contour graphs are plotted.
$\varphi ^{6}$model expansion method, complex GinzburgLandau equation, soliton solutions, dual powerlaw nonlinearity
Primary Language  English 

Subjects  Numerical Solution of Differential and Integral Equations, Numerical and Computational Mathematics (Other) 
Journal Section  Research Articles 
Authors 

Publication Date  September 30, 2023 
Submission Date  March 16, 2023 
Published in Issue  Year 2023 Volume: 3 Issue: 3 