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<p>This paper presents a numerical framework in MATLAB for solving the generalized nonlinear Schrödinger equation (GNLSE) using adaptive algorithms and the split Fourier method. It simulates soliton-wave interactions in optical fibers, taking into account high-order dispersion (HOD), nonlinear mechanisms (such as SPM, Raman, and Brillion), and the effect of soliton initial divergence. The results show that the dispersion coefficients (<i>β</i>₂ and <i>β</i>₄) govern the stability and interactions of solitons, causing phenomena such as spectrum splitting and the formation of dispersive waves. Mechanisms for controlling soliton fusion/repulsion via initial separation and relative phase are also revealed, with typical accuracy &lt; 0.1%. The framework offers a computational speedup of up to 10 times, supporting the design of optical communication systems, frequency combs, and pulse compressors. The model can be generalized to study quantum phase transitions and soliton interactions in multilayer photonic crystals, with potential extension for future algebraic modeling.</p>

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Nonlinear and dispersive effects on dark soliton interaction in photonic crystal fiber

  • 期刊论文

  • 发表日期：

    2025年7月2日

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  • Mohammed Salim Jasim AL-Taie

摘要

This paper presents a numerical framework in MATLAB for solving the generalized nonlinear Schrödinger equation (GNLSE) using adaptive algorithms and the split Fourier method. It simulates soliton-wave interactions in optical fibers, taking into account high-order dispersion (HOD), nonlinear mechanisms (such as SPM, Raman, and Brillion), and the effect of soliton initial divergence. The results show that the dispersion coefficients (β₂ and β₄) govern the stability and interactions of solitons, causing phenomena such as spectrum splitting and the formation of dispersive waves. Mechanisms for controlling soliton fusion/repulsion via initial separation and relative phase are also revealed, with typical accuracy < 0.1%. The framework offers a computational speedup of up to 10 times, supporting the design of optical communication systems, frequency combs, and pulse compressors. The model can be generalized to study quantum phase transitions and soliton interactions in multilayer photonic crystals, with potential extension for future algebraic modeling.