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<p>This paper presents a study on spatiotemporal solitons (light bullets) in nonlinear metamaterial waveguides, modeled by a modified (3+1)-dimensional cubic-quintic complex Ginzburg–Landau [(3+1)D CQ-CGL] equation. The model incorporates higher-order corrections and an external potential, the latter arising from a combination of linear refractive index modulation and transverse viscosity-induced frictional force. We treat these effects as perturbations within a variational approach for dissipative systems, complemented by direct numerical simulations. Our analysis confirms the feasibility of stable light bullet formation in such media. By applying the Routh–Hurwitz stability criterion and constructing bifurcation diagrams, we identify optimal parameter ranges for the quintic self-steepening and linear potential coefficients that facilitate stable propagation. Both analytical and numerical results demonstrate that the formation of light bullet complexes is deeply governed by the interplay between quintic self-steepening and the external potential.</p>

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Control of self-steepening effects on dissipative light bullets via linear potential in a (3+1)D Ginzburg–Landau model

  • 期刊论文

  • 发表日期：

    2025年12月15日

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  • Eric Martial Signé,
  • Alain Djazet,
  • Laure Tiam Megne,
  • Martin Djoko,
  • Serge Ibraïd Fewo,
  • Timoléon Crépin Kofané

摘要

This paper presents a study on spatiotemporal solitons (light bullets) in nonlinear metamaterial waveguides, modeled by a modified (3+1)-dimensional cubic-quintic complex Ginzburg–Landau [(3+1)D CQ-CGL] equation. The model incorporates higher-order corrections and an external potential, the latter arising from a combination of linear refractive index modulation and transverse viscosity-induced frictional force. We treat these effects as perturbations within a variational approach for dissipative systems, complemented by direct numerical simulations. Our analysis confirms the feasibility of stable light bullet formation in such media. By applying the Routh–Hurwitz stability criterion and constructing bifurcation diagrams, we identify optimal parameter ranges for the quintic self-steepening and linear potential coefficients that facilitate stable propagation. Both analytical and numerical results demonstrate that the formation of light bullet complexes is deeply governed by the interplay between quintic self-steepening and the external potential.