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<p>To address the limitation of the constant-coefficient fourth-order nonlinear Schrödinger equation (NLSE) in describing the complex propagation behaviors in inhomogeneous optical systems, we extend a constant-coefficient fourth-order NLSE to a variable-coefficient form in this paper. The dynamic characteristics and intrinsic physical mechanisms of solitons and soliton molecules governed by that extended equation in an inhomogeneous medium are systematically investigated. Under the integrability constraint conditions, that extended equation is transformed into a bilinear form via the Hirota bilinear method with an auxiliary function, from which the analytical <i>N</i>-soliton solutions are derived. A key finding is the dual-parameter cooperative adjustment mechanism, through which the generation of diverse soliton structures and the regulation of complex multi-soliton behaviors can be achieved, including the soliton molecule formation via velocity resonance, adjustable energy exchange, fission, and periodic oscillation. These research findings exhibit application potential in optical communication and signal processing, including all-optical amplification, optical switching, and optical path adjustment.</p>

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Soliton and soliton molecule dynamics in a higher-order dispersion variable-coefficient optical fiber model

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Na Shi,
  • Houhui Yi,
  • Bo Tian,
  • Muwei Liu,
  • Yan Jiang

摘要

To address the limitation of the constant-coefficient fourth-order nonlinear Schrödinger equation (NLSE) in describing the complex propagation behaviors in inhomogeneous optical systems, we extend a constant-coefficient fourth-order NLSE to a variable-coefficient form in this paper. The dynamic characteristics and intrinsic physical mechanisms of solitons and soliton molecules governed by that extended equation in an inhomogeneous medium are systematically investigated. Under the integrability constraint conditions, that extended equation is transformed into a bilinear form via the Hirota bilinear method with an auxiliary function, from which the analytical N-soliton solutions are derived. A key finding is the dual-parameter cooperative adjustment mechanism, through which the generation of diverse soliton structures and the regulation of complex multi-soliton behaviors can be achieved, including the soliton molecule formation via velocity resonance, adjustable energy exchange, fission, and periodic oscillation. These research findings exhibit application potential in optical communication and signal processing, including all-optical amplification, optical switching, and optical path adjustment.