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<p>This study investigates nonlinear wave propagation in nonlocal magneto-electro-elastic (MEE) sandwich nanoplates using an extended version of the Yan–Dowell framework. The governing equations account for nonlocal elasticity and multiphysical coupling, allowing for a precise description of size-dependent effects and electromechanical interactions at the nanoscale. A harmonic wave approach is used to obtain the dispersion relation, with subsequent analysis of phase and group velocities. Instability of modulation is examined, revealing a bounded instability band shaped by the balance between dispersion and nonlinearity. The impact of the nonlocal parameter and MEE coupling on bandwidth, critical wave number, and growth rate is analyzed. The nonlinear Schrödinger equation is then derived to model envelope dynamics, yielding stable envelope soliton solutions. Numerical findings indicate that soliton width and energy concentration can be adjusted via MEE coupling, enabling targeted control over wave behavior. Compared to linear wave packets, solitons exhibit enhanced localization and stability. The developed model offers a comprehensive approach for studying nonlinear wave phenomena in multifunctional nanostructures for wave guidance, energy transmission, and smart materials applications.</p>

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Dispersion, instability, and soliton dynamics in nonlocal MEE nanoplates

  • 期刊论文

  • 发表日期：

    2026年7月8日

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  • R. Karthikeyan,
  • R. Selvamani,
  • Samia Elattar,
  • M. Ijaz Khan

摘要

This study investigates nonlinear wave propagation in nonlocal magneto-electro-elastic (MEE) sandwich nanoplates using an extended version of the Yan–Dowell framework. The governing equations account for nonlocal elasticity and multiphysical coupling, allowing for a precise description of size-dependent effects and electromechanical interactions at the nanoscale. A harmonic wave approach is used to obtain the dispersion relation, with subsequent analysis of phase and group velocities. Instability of modulation is examined, revealing a bounded instability band shaped by the balance between dispersion and nonlinearity. The impact of the nonlocal parameter and MEE coupling on bandwidth, critical wave number, and growth rate is analyzed. The nonlinear Schrödinger equation is then derived to model envelope dynamics, yielding stable envelope soliton solutions. Numerical findings indicate that soliton width and energy concentration can be adjusted via MEE coupling, enabling targeted control over wave behavior. Compared to linear wave packets, solitons exhibit enhanced localization and stability. The developed model offers a comprehensive approach for studying nonlinear wave phenomena in multifunctional nanostructures for wave guidance, energy transmission, and smart materials applications.