Nonlinear Dynamics in Periodically Distributed Fibre Amplification Systems
Abstract
We investigate effects of longitudinally varying nonlinearity on periodically distributed amplification systems in optical fibres. Emphasis is made on configurations in which the nonlinear coefficient exponentially grows or decays along the propagation distance, while the group-velocity-dispersion (GVD) coefficient is held constant. Such systems are of practical relevance to the design of highly efficient nonlinear devices, including broadband light sources and advanced amplification schemes, where precise management of the interplay between the GVD, nonlinearity, and gain is essential. Adopting the known generic integrability condition, we derive exact analytical expressions for the evolution of the optical field in the presence of the tailored nonlinearity profiles and periodically distributed gain. The resulting periodic wavetrain solutions and their long-wave limit in the form of bright and dark solitons provide insight into the controlled enhancement or suppression of nonlinear effects under realistic amplification conditions. The robustness of these solutions is examined by introducing finite perturbations and directly evaluating their effects on the corresponding intensity profiles. The structural stability of solutions against deviations from the integrability condition is demonstrated too. Outcomes of this study contribute to a deeper understanding of the nonlinear pulse dynamics in engineered gain-managed fibres and offer guidance for the development of novel optical systems, where the spatial distribution of the nonlinearity is exploited to optimise the performance.
Related
- Stability Analysis and Synchronization of Distributed-Order Fractional Nonlinear Dynamical Systems with Time Delay
- The role of distributed friction dynamics on heave-induced motion of offshore drilling systems: modelling, analysis, and simulations
- Methods for Deriving Nonlinear Kinetic Equations from the Dynamics of Quantum Systems
- Zeros of Melnikov functions for periodically perturbed Hamiltonian systems with random coefficients
- Characterization and Monitoring of Nonlinear Dynamics and Chaos in Complex Physiological Systems
BibTeX
@misc{atuba2026nonlinear,
title = {{Nonlinear Dynamics in Periodically Distributed Fibre Amplification Systems}},
author = {Sunday O. Atuba and Boris A. Malomed},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01159},
eprint = {2611.01159},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01159},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Nonlinear Dynamics in Periodically Distributed Fibre Amplification Systems
AU - Sunday O. Atuba
AU - Boris A. Malomed
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01159
UR - https://arxiv.org/abs/2611.01159
AB - We investigate effects of longitudinally varying nonlinearity on periodically distributed amplification systems in optical fibres. Emphasis is made on configurations in which the nonlinear coefficient exponentially grows or decays along the propagation distance, while the group-velocity-dispersion (GVD) coefficient is held constant. Such systems are of practical relevance to the design of highly efficient nonlinear devices, including broadband light sources and advanced amplification schemes, where precise management of the interplay between the GVD, nonlinearity, and gain is essential. Adopting the known generic integrability condition, we derive exact analytical expressions for the evolution of the optical field in the presence of the tailored nonlinearity profiles and periodically distributed gain. The resulting periodic wavetrain solutions and their long-wave limit in the form of bright and dark solitons provide insight into the controlled enhancement or suppression of nonlinear effects under realistic amplification conditions. The robustness of these solutions is examined by introducing finite perturbations and directly evaluating their effects on the corresponding intensity profiles. The structural stability of solutions against deviations from the integrability condition is demonstrated too. Outcomes of this study contribute to a deeper understanding of the nonlinear pulse dynamics in engineered gain-managed fibres and offer guidance for the development of novel optical systems, where the spatial distribution of the nonlinearity is exploited to optimise the performance.
ER -