These are some of the key papers related to our work:

Nonlinear waves in layered media

• LY Solitary waves in layered nonlinear media
• KL Shock Dynamics in Layered Periodic Media
• QK Numerical simulation of cylindrical solitary waves in periodic media
• Qthesis Nonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media
• Kthesis High Order Strong Stability Preserving Time Integrators and Numerical Wave Propagation Methods for Hyperbolic PDEs – see Chapter 10
• LY Phase Plane Behavior of Solitary Waves in Nonlinear Layered Media

Higher-order homogenization of wave equations

• YK Solving Boundary-Value Problems for Systems of Hyperbolic Conservation Laws with Rapidly Varying Coefficients
• SS A Dispersive Effective Medium for Wave Propagation in Periodic Composites
• FC Higher-Order Homogenization of Initial/Boundary-Value Problem
• CF A dispersive model for wave propagation in periodic heterogeneous media based on homogenization with multiple spatial and temporal scales

Shock waves in heterogeneous media

• EGKKK The theory of optical dispersive shock waves in photorefractive media
• SW Coherent Structures and Carrier Shocks in the Nonlinear Periodic Maxwell Equations

Experimental work

• An experimental investigation of shock wave propagation in periodically layered composites
• Scattering as a mechanism for structured shock waves in metals
• The effect of heterogeneity on plane wave propagation through layered composites

Shallow water waves over bathymetry (periodic or random)

• Time reversing solitary waves
• Shock structure due to stochastic forcing and the time reversal of nonlinear waves
• Effective Behavior of Solitary Waves over Random Topography
• Time-reversed refocusing of surface water waves

Computing dispersion relations

• An Efficient Finite Element Method for Computing Spectra of Photonic and Acoustic Band-Gap Materials
• An efficient method for band structure calculations in 3D photonic crystals
• Floquet Multipliers of Periodic Waveguides via Dirichlet-to-Neumann Maps

Pseudospectral methods

Finite volume methods