Mathematics (Sep 2024)
New Coupled Optical Solitons to Birefringent Fibers for Complex Ginzburg–Landau Equations with Hamiltonian Perturbations and Kerr Law Nonlinearity
Abstract
In this study, we use an analytical method tailored for the in-depth exploration of coupled nonlinear partial differential equations (NLPDEs), with a primary focus on the dynamics of solitons. Traditional methods are quite effective for solving individual nonlinear partial differential equations (NLPDEs). However, their performance diminishes notably when addressing systems of coupled NLPDEs. This decline in effectiveness is mainly due to the complex interaction terms that arise in these coupled systems. Commonly, researchers have attempted to simplify coupled NLPDEs into single equations by imposing proportional relationships between various solutions. Unfortunately, this simplification often leads to a significant deviation from the true physical phenomena that these equations aim to describe. Our approach is distinctively advantageous in its straightforwardness and precision, offering a clearer and more insightful analytical perspective for examining coupled NLPDEs. It is capable of concurrently facilitating the propagation of different soliton types in two distinct systems through a single process. It also supports the spontaneous emergence of similar solitons in both systems with minimal restrictions. It has been extensively used to investigate a wide array of new coupled progressive solitons in birefringent fibers, specifically for complex Ginzburg–Landau Equations (CGLEs) involving Hamiltonian perturbations and Kerr law nonlinearity. The resulting solitons, with comprehensive 2D and 3D visualizations, showcase a variety of coupled soliton configurations, including several that are unprecedented in the field. This innovative approach not only addresses a significant gap in existing methodologies but also broadens the horizons for future research in optical communications and related disciplines.
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