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Updated: May 17, 2026

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
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Dispersive shock waves in periodic lattices.

Su Yang1, Sathyanarayanan Chandramouli1, P G Kevrekidis2

  • 1University of Massachusetts, Department of Mathematics and Statistics, Amherst, Massachusetts 01003-4515, USA.

Physical Review. E
|May 16, 2026
PubMed
Summary

We studied dispersive shock waves in nonlinear systems using a discrete model. This approach accurately captures wave dynamics in periodic potentials, revealing complex hydrodynamic phenomena.

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Area of Science:

  • Nonlinear Physics
  • Wave Phenomena
  • Condensed Matter Physics

Background:

  • Dispersive shock waves (DSWs) occur in nonlinear systems like optical lattices and superfluids.
  • The nonlinear Schrödinger (NLS) equation with periodic potentials models these phenomena.
  • Understanding DSWs is crucial for applications in optics and quantum fluids.

Purpose of the Study:

  • To investigate the generation and dynamics of DSWs in a nonlinear Schrödinger equation with a periodic potential.
  • To develop and validate a reduced discrete model for analyzing these wave phenomena.
  • To explore the rich spectrum of discrete dispersive hydrodynamic behaviors.

Main Methods:

  • Utilized the tight-binding approximation to reduce the continuous NLS model to a discrete NLS (DNLS) model.
  • Employed Whitham modulation theory and long-wave quasicontinuum reductions for analysis.
  • Compared the discrete model's predictions with the continuous model's phenomenology.

Main Results:

  • The tight-binding approximation shows higher fidelity for deeper periodic potentials.
  • The reduced DNLS model accurately captures dynamics at the potential minima.
  • A rich spectrum of nonconvex, discrete dispersive hydrodynamic phenomena was uncovered.

Conclusions:

  • The discrete nonlinear Schrödinger model provides an effective framework for studying DSWs in periodic potentials.
  • This work bridges the gap between continuous and discrete models for wave dynamics.
  • The findings offer insights into wave propagation in structured nonlinear media.