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<p>This work has investigated a partially nonlocal, variable-coefficient coupled nonlinear Schrödinger equation, which models wave propagation in inhomogeneous optical fibers. The bilinear form of the equation has been derived using the Hirota method, and its multi-soliton solutions have been simulated numerically. Subsequently, based on linear stability analysis, we have conducted modulational instability (MI) and cascading instability (CI) analyses. The systematic investigation of the MI gain reveals that the amplitude <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(A_s (s=1,2)\)</EquationSource> </InlineEquation> influences the width of the MI band, while the wavenumber <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(k_s\)</EquationSource> </InlineEquation> governs its spectral position. Furthermore, both the group velocity dispersion and nonlinear parameters have been found to affect the gain bandwidth and the peak gain value. The functional forms of the variable coefficients also play a critical role in shaping the MI gain spectrum. Under periodic boundary conditions, the system exhibits a cascading process, enabling the prediction of the first breather’s emergence time through an analysis of the leading Fourier modes. Direct numerical simulations have confirmed the formation of this initial breather, followed by the recurrence of multiple subsequent breathers. These findings provide valuable insights into soliton dynamics in nonlinear optical fibers and related physical systems.</p>

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Modulational and cascading instability in coupled nonlinear Schrödinger systems in inhomogeneous optical fibers

  • 期刊论文

  • 发表日期：

    2026年3月14日

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  • Meng-Lin Zhang,
  • Da-Wei Zuo

摘要

This work has investigated a partially nonlocal, variable-coefficient coupled nonlinear Schrödinger equation, which models wave propagation in inhomogeneous optical fibers. The bilinear form of the equation has been derived using the Hirota method, and its multi-soliton solutions have been simulated numerically. Subsequently, based on linear stability analysis, we have conducted modulational instability (MI) and cascading instability (CI) analyses. The systematic investigation of the MI gain reveals that the amplitude \(A_s (s=1,2)\) influences the width of the MI band, while the wavenumber \(k_s\) governs its spectral position. Furthermore, both the group velocity dispersion and nonlinear parameters have been found to affect the gain bandwidth and the peak gain value. The functional forms of the variable coefficients also play a critical role in shaping the MI gain spectrum. Under periodic boundary conditions, the system exhibits a cascading process, enabling the prediction of the first breather’s emergence time through an analysis of the leading Fourier modes. Direct numerical simulations have confirmed the formation of this initial breather, followed by the recurrence of multiple subsequent breathers. These findings provide valuable insights into soliton dynamics in nonlinear optical fibers and related physical systems.