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<p>This article investigates an extended stochastic nonlinear Schrödinger equation (NLSE), which incorporates higher-order dispersion, quantitative higher-order nonlinearity, and multiplicative white noise. For the first time, the polynomial complete discriminant system and the trial equation method are applied to this model. Without presupposing the form of solutions, a comprehensive set of exact solutions is derived, including triangular periodic solutions, kink/bell-shaped solitons, and rational singular solutions. Dynamical analysis confirms the coexistence of solitons and periodic modes. Lyapunov exponents reveal perturbation-induced chaos, with the quintic nonlinear coefficient <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(c_{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>c</mi> <mn>3</mn> </msub> </math></EquationSource> </InlineEquation>, a key parameter of quantitative nonlinearity, exerting a significant influence. Stochastic averaging analysis indicates that white noise disrupts soliton characteristics, leading to amplitude decay and delays that correlate with nonlinear coefficients. This work enriches the theory of stochastic nonlinear systems, establishes a ‘noise-soliton-chaos’ model, and provides insights for anti-interference strategies in optical soliton communication and noise control in quantum optics.</p>

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Stochastic nonlinear Schrödinger equation with the higher-order effects: Solitons, noise-induced chaos and their optical-communication implications

  • 期刊论文

  • 发表日期：

    2026年6月19日

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  • LIU Shirong

摘要

This article investigates an extended stochastic nonlinear Schrödinger equation (NLSE), which incorporates higher-order dispersion, quantitative higher-order nonlinearity, and multiplicative white noise. For the first time, the polynomial complete discriminant system and the trial equation method are applied to this model. Without presupposing the form of solutions, a comprehensive set of exact solutions is derived, including triangular periodic solutions, kink/bell-shaped solitons, and rational singular solutions. Dynamical analysis confirms the coexistence of solitons and periodic modes. Lyapunov exponents reveal perturbation-induced chaos, with the quintic nonlinear coefficient \(c_{3}\) c 3 , a key parameter of quantitative nonlinearity, exerting a significant influence. Stochastic averaging analysis indicates that white noise disrupts soliton characteristics, leading to amplitude decay and delays that correlate with nonlinear coefficients. This work enriches the theory of stochastic nonlinear systems, establishes a ‘noise-soliton-chaos’ model, and provides insights for anti-interference strategies in optical soliton communication and noise control in quantum optics.