Propagation of solitons and nonlinear behavior in nonlinear power law fibers
DOI:
https://doi.org/10.64700/altay.21Keywords:
\(\varphi ^{6}\)-model expansion approach, the complex Ginzburg--Landau equation, traveling wave solution, power law nonlinearityAbstract
This study investigates soliton propagation within the framework of nonlinear optics, specifically under the influence of a detuning parameter modeled by the complex Ginzburg–Landau equation (CGLE). Employing the $\varphi ^{6}$-model expansion method, we derive a diverse set of analytical solutions, including trigonometric, hyperbolic, and rational function solutions. Notably, singular soliton solutions are obtained and shown to exhibit positive characteristics. The analysis is conducted in the context of nonlinear optical fibers governed by a power-law nonlinearity. The results contribute to a deeper understanding of the nonlinear dynamical behavior inherent in the CGLE and highlight the effectiveness of the applied method as a robust and efficient tool for obtaining reliable solutions to a wide class of nonlinear partial differential equations. To illustrate the physical features of the obtained solutions, several representative results are visualized through two-dimensional, three-dimensional, and contour plots.
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