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<p>This work conducts a rigorous analytical study of nonlinear wave propagation in highly dispersive optical couplers incorporating power-law metamaterials. The coupled nonlinear evolution model governing the system is addressed using Kudryashov’s addendum method, enabling the derivation of new exact soliton solutions in closed form. The analytical treatment reveals three distinct soliton families—bright, singular, and hybrid bright–singular solitons—each emerging under specific parametric regimes defined by the interplay between high-order dispersion and power-law nonlinearity. The results uncover a rich solution structure and provide insight into the mathematical mechanisms that govern soliton admissibility, formation, and qualitative behavior in metamaterial-based photonic media. Beyond establishing new explicit solutions, the study highlights the critical influence of nonlinearity order and metamaterial response on solution morphology, thus offering a theoretical framework applicable to broader classes of nonlocal, non-Kerr, and engineered nonlinear optical systems. These findings lay the foundation for further analytical, numerical, and stability investigations in advanced metamaterial-driven soliton dynamics.</p>

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Soliton propagation and interaction in highly dispersive power-law optical metamaterial couplers via Kudryashov’s Addendum method

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Mohamed E. M. Alngar

摘要

This work conducts a rigorous analytical study of nonlinear wave propagation in highly dispersive optical couplers incorporating power-law metamaterials. The coupled nonlinear evolution model governing the system is addressed using Kudryashov’s addendum method, enabling the derivation of new exact soliton solutions in closed form. The analytical treatment reveals three distinct soliton families—bright, singular, and hybrid bright–singular solitons—each emerging under specific parametric regimes defined by the interplay between high-order dispersion and power-law nonlinearity. The results uncover a rich solution structure and provide insight into the mathematical mechanisms that govern soliton admissibility, formation, and qualitative behavior in metamaterial-based photonic media. Beyond establishing new explicit solutions, the study highlights the critical influence of nonlinearity order and metamaterial response on solution morphology, thus offering a theoretical framework applicable to broader classes of nonlocal, non-Kerr, and engineered nonlinear optical systems. These findings lay the foundation for further analytical, numerical, and stability investigations in advanced metamaterial-driven soliton dynamics.