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<p>Existing theoretical frameworks for wave propagation in structured continua typically treat nonlinear steepening, governed by Riemann wave equations, and dispersive regularization, described by Korteweg-de Vries equations, as isolated phenomena. This separation inherently limits their capacity to accurately model complex micro-strain dynamics where both mechanisms operate concurrently and interact fundamentally. The present study introduces and rigorously examines a newly formulated nonlinear Riemann–Korteweg-de Vries hybrid (R–KdV–H) equation that coherently integrates compressive nonlinearity with dispersive smoothing within a unified evolutionary framework. The proposed model uniquely captures the intricate competition between wave steepening and dispersion-induced spreading, which proves essential for characterizing localized micro-strain pulses and solitary wave structures in condensed media, metamaterials, and nonlinear optical systems. Exact analytical solutions are systematically constructed through the Khater II method, a technique particularly suited for revealing explicit traveling-wave profiles and parametric families of both stable solitary waves and quasi-periodic modes that emerge from the nonlinear-dispersive interplay. The Hamiltonian structure is derived explicitly to establish energy conservation principles and to examine the dynamical stability of the obtained wave profiles through comprehensive spectral analysis. Numerical simulations conducted across varying nonlinearity and dispersion parameters illuminate critical transition regimes where soliton formation exhibits either enhancement or suppression, thereby revealing the sensitive dependence of wave dynamics on system parameters. These findings collectively establish both the physical relevance and mathematical rigor of the hybrid model, providing a validated analytical framework for investigating micro-strain wave propagation in structured continua. The results offer direct applications to shock mitigation strategies in metamaterials, pulse propagation in nonlinear optics, and the broader understanding of dispersive nonlinear systems where multiple physical mechanisms compete and coexist.</p>

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Hybrid wave coherence: nonlinear dynamics underpinning optical and quantum stability

  • 期刊论文

  • 发表日期：

    2026年2月21日

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  • Mostafa M. A. Khater

摘要

Existing theoretical frameworks for wave propagation in structured continua typically treat nonlinear steepening, governed by Riemann wave equations, and dispersive regularization, described by Korteweg-de Vries equations, as isolated phenomena. This separation inherently limits their capacity to accurately model complex micro-strain dynamics where both mechanisms operate concurrently and interact fundamentally. The present study introduces and rigorously examines a newly formulated nonlinear Riemann–Korteweg-de Vries hybrid (R–KdV–H) equation that coherently integrates compressive nonlinearity with dispersive smoothing within a unified evolutionary framework. The proposed model uniquely captures the intricate competition between wave steepening and dispersion-induced spreading, which proves essential for characterizing localized micro-strain pulses and solitary wave structures in condensed media, metamaterials, and nonlinear optical systems. Exact analytical solutions are systematically constructed through the Khater II method, a technique particularly suited for revealing explicit traveling-wave profiles and parametric families of both stable solitary waves and quasi-periodic modes that emerge from the nonlinear-dispersive interplay. The Hamiltonian structure is derived explicitly to establish energy conservation principles and to examine the dynamical stability of the obtained wave profiles through comprehensive spectral analysis. Numerical simulations conducted across varying nonlinearity and dispersion parameters illuminate critical transition regimes where soliton formation exhibits either enhancement or suppression, thereby revealing the sensitive dependence of wave dynamics on system parameters. These findings collectively establish both the physical relevance and mathematical rigor of the hybrid model, providing a validated analytical framework for investigating micro-strain wave propagation in structured continua. The results offer direct applications to shock mitigation strategies in metamaterials, pulse propagation in nonlinear optics, and the broader understanding of dispersive nonlinear systems where multiple physical mechanisms compete and coexist.