Scholarlink

<p>This study examines bifurcation structures, optical soliton solutions, chaotic dynamics, and sensitivity analysis for a third-order (1+1)-dimensional nonlinear Schrödinger equation with power-law self-phase modulation, spatio-temporal dispersion, and inter-modal dispersion, neglecting chromatic dispersion. A traveling-wave transformation reduces the model to a singular dynamical system, which is regularized through a suitable change of the independent variable; both systems have the same first integrals. Bifurcation theory for planar systems is applied to analyze the corresponding phase portraits. The modified extended hyperbolic function method yields new exact traveling-wave solutions, including exponential, bright, singular, and single-periodic forms. Chaotic behavior is investigated via Poincaré sections, bifurcation diagrams and Lyapunov exponents, together with a detailed analysis of sensitivity to initial conditions. The results broaden the understanding of nonlinear wave propagation in optical media, with applications in quantum optics, nonlinear optics, and plasma physics. Unlike Hamad and Ali (<CitationRef CitationID="CR21">2025b</CitationRef>), who considered only <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n=1\)</EquationSource> </InlineEquation>, this work addresses a general nonlinearity index.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Dynamical behavior and exact solutions of the third-order (1+1)-dimensional nonlinear Schrödinger equation with general power-law non linearity

  • 期刊论文

  • 发表日期：

    2026年7月10日

查看全文
  • Ibrahim S. Hamad,
  • Karmina K. Ali

摘要

This study examines bifurcation structures, optical soliton solutions, chaotic dynamics, and sensitivity analysis for a third-order (1+1)-dimensional nonlinear Schrödinger equation with power-law self-phase modulation, spatio-temporal dispersion, and inter-modal dispersion, neglecting chromatic dispersion. A traveling-wave transformation reduces the model to a singular dynamical system, which is regularized through a suitable change of the independent variable; both systems have the same first integrals. Bifurcation theory for planar systems is applied to analyze the corresponding phase portraits. The modified extended hyperbolic function method yields new exact traveling-wave solutions, including exponential, bright, singular, and single-periodic forms. Chaotic behavior is investigated via Poincaré sections, bifurcation diagrams and Lyapunov exponents, together with a detailed analysis of sensitivity to initial conditions. The results broaden the understanding of nonlinear wave propagation in optical media, with applications in quantum optics, nonlinear optics, and plasma physics. Unlike Hamad and Ali (2025b), who considered only \(n=1\) , this work addresses a general nonlinearity index.