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Weakly nonlinear plane waves are considered in hyperelastic crystals. Evolution equations are derived at a quadratically nonlinear level for the amplitudes of quasi-longitudinal and quasi-transverse waves propagating in arbitrary…
The two-dimensional propagation of small-amplitude waves through an infinite periodic array of freely-floating rectangular floes is considered under the assumptions of inviscid linearised wave theory. Fluid gaps between adjacent floes allow…
Wave propagation in one-dimensional heterogeneous bistable media is studied using the Schl\"ogl model as a representative example. Starting from the analytically known traveling wave solution for the homogeneous medium, infinitely extended,…
Energy transmission over long distances by waves is a key mechanism for many natural processes. This possibility arises when an inhomogeneous medium is arranged in such a manner that it enables a certain type of wave to propagate with…
The before described general principles and methodology of calculating electron wave propagation in homogeneous isotropic half-infinity slab of Maxwellian plasma with indefinite but in principal value sense taken integrals in characteristic…
The nonlinear dynamics of the free surface of an ideal dielectric liquid in a strong electric field is studied. The equation for the evolution of surface electrohydrodynamic waves is derived in the approximation of small surface-slope…
This pedagogical paper presents a comprehensive framework for interpreting dispersion relations across fundamental physical systems. We adopt a novel approach that starts from the mathematical form $\omega(\mathbf{k})$ and systematically…
We theoretically describe the quasi one-dimensional transverse spreading of a light pulse propagating in a nonlinear optical material in the presence of a uniform background light intensity. For short propagation distances the pulse can be…
We propose a mathematical framework to systematically explore the propagation properties of a class of continuous in time nonlinear neural network models comprising a hierarchy of processing areas, mutually connected according to the…
Waves play an essential role in many aspects of plasma science, such as plasma manipulation and diagnostics. Due to the complexity of the governing equations, approximate models are often necessary to describe wave dynamics. In this…
The propagation of water waves of finite depth and flat bottom is studied in the case when the depth is not small in comparison to the wavelength. This propagation regime is complementary to the long-wave regime described by the famous KdV…
We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…
The current paper is devoted to the investigation of wave propagation phenomenon in reaction-diffusion equations with ignition type nonlinearity in time heterogeneous and random media. It is proven that such equations in time heterogeneous…
A one-way wave equation is an evolution equation in one of the space directions that describes (approximately) a wave field. The exact wave field is approximated in a high frequency, microlocal sense. Here we derive the pseudodifferential…
Characterizing electromagnetic wave propagation in nonlinear and inhomogeneous media is of great interest from both theoretical and practical perspectives, even though it is extremely complicated. In fact, it is still an unresolved issue to…
The Wigner Transform (WT) has been extensively used in the formulation of phase-space models for a variety of wave propagation problems including high-frequency limits, nonlinear and random waves. It is well known that the WT features…
Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is…
The Whitham equation is a nonlocal, nonlinear partial differential equation that models the temporal evolution of spatial profiles of surface displacement of water waves. However, many laboratory and field measurements record time series at…
We extend the usual derivation of the wave equation from Maxwell's equations in vacuum to the case of electromagnetic fields in dispersive homogeneous isotropic linear media. Usually, dispersive properties of materials are studied in…
The dispersion equation of MGD plasma waves measured in a reference frame with a relative speed from that where they are generated is derived. The analysis leads further from what is known for waves produced in stationary plasmas in the…