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<p>In this paper, we present an analytical framework to control soliton interactions in optical fibers derived from the generalized higher-order nonlinear Schrödinger (GHNLS) equation, where both septimal and weakly nonlocal nonlinear effects are incorporated. Our approach involves a bilinear formulation based on the Hirota method, which allows us to derive branching bound-state structures compactly and systematically. The formulation captures the combined effects of higher-order self-phase modulation and extended spatial nonlinear effects, which are generally overlooked in traditional bilinear approaches. We derive analytical expressions for single and double-soliton solutions, revealing parameter-dependent control over localized two-soliton interaction patterns and Y-type interaction thresholds through the septimal (Φ) and nonlocal (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Upsilon \)</EquationSource> </InlineEquation>) coefficients. By performing linear stability analysis using Fourier collocation-based techniques, we also identify transitions from stable to unstable regimes. These results provide insight into soliton interaction dynamics and have potential applications in ultrafast optical switching and supercontinuum generation in fiber-optic systems.</p>

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Dynamics of localized two-soliton interactions and Y-type structures in nonlocal optical media with septimal nonlinearity

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • R. Ravichandran,
  • E. Parasuraman,
  • O. S. Raja Mohan,
  • Zehra Pinar Izgi

摘要

In this paper, we present an analytical framework to control soliton interactions in optical fibers derived from the generalized higher-order nonlinear Schrödinger (GHNLS) equation, where both septimal and weakly nonlocal nonlinear effects are incorporated. Our approach involves a bilinear formulation based on the Hirota method, which allows us to derive branching bound-state structures compactly and systematically. The formulation captures the combined effects of higher-order self-phase modulation and extended spatial nonlinear effects, which are generally overlooked in traditional bilinear approaches. We derive analytical expressions for single and double-soliton solutions, revealing parameter-dependent control over localized two-soliton interaction patterns and Y-type interaction thresholds through the septimal (Φ) and nonlocal ( \(\Upsilon \) ) coefficients. By performing linear stability analysis using Fourier collocation-based techniques, we also identify transitions from stable to unstable regimes. These results provide insight into soliton interaction dynamics and have potential applications in ultrafast optical switching and supercontinuum generation in fiber-optic systems.