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In the context of forecasting temperature and pressure fields in high-intensity focussed ultrasound, the accuracy of predictive models is critical for the safety and efficacy of treatment. In such fields inertial cavitation is often…
In this work we formulate a generalized theoretical model to describe the nonlinear dynamics observed in combined frequency-amplitude modulators whose characteristic parameters exhibit a nonlinear dependence on the input modulating signal.…
The repulsion between free electrons inside a metal makes its optical response spatially dispersive, so that it is not described by Drude's model but by a hydrodynamic model. We give here fully analytic results for a metallic slab in this…
The influence of quantum fluctuations of the electromagnetic field on the propagation of a polarized light wave in a nonlinear dielectric is investigated. It is shown that in some cases, the fluctuations couple to the optical nonlinearities…
Nonlinearity is the key to introducing novel concepts in various technologies utilizing traveling waves. In contrast to the field of optics, where highly functional devices have been developed using optical Kerr nonlinearity, such a…
We derive the nonlinear fractional surface wave equation that governs compression waves at an interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective…
We investigate the spatio-temporal evolution of a Gaussian probe pulse propagating through a four-level $N$-type atomic medium. At two-photon resonance of probe-and control fields, weaker probe pulses may propagate through the medium with…
Nonlocal nonlinear Schroedinger-type equation is derived as a model to describe paraxial light propagation in nonlinear media with different `degrees' of nonlocality. High frequency limit of this equation is studied under specific…
The problem of light propagation of frequency corresponding to half of the energy difference between a metastable excited state and the ground state of atoms is examined, and solved for coherent medium by analytic means. We demonstrate that…
Ranges of existence and stability of dark cavity-soliton stationary states in a Fabry-Perot resonator with a Kerr nonlinear medium and normal dispersion are determined. The Fabry-Perot configuration introduces nonlocal coupling that shifts…
An analytical approach based on the parametric representation of the wave propagation in nonuniform media was considered. In addition to the previously developed theory of parametric antiresonance describing the field attenuation in stop…
Complex elastic media such as biological membranes, in particular, blood vessels, may be described as fiber-reinforced solids in the framework of nonlinear hyperelasticity. Finite axially symmetric anti-plane shear displacements in such…
Wood's anomaly is a fundamental wave phenomenon that stems from the interplay between farfields and surface-wave (SW) resonances through structured interfaces. Recent theories have suggested temporal analogs of such SW coupling processes by…
We investigate how Rayleigh waves interact with modulated resonators located on the free surface of a semi-infinite elastic medium. We begin by studying the dynamics of a single resonator with time-modulated stiffness. In particular, we…
Space-time materials are obtained by modulating a physical medium with a traveling-wave perturbation of one or several of its constitutive parameters, such as the density or the bulk modulus in the case of acoustic materials. When this…
We study the nonlinear optical propagation of two different classes of space-varying polarized light beams -- radially symmetric vector beams and Poincar\'e beams with lemon and star topologies -- in a rubidium vapour cell. Unlike…
We present a theory for wave scintillation in the situation with a time-dependent partially coherent source and a time-dependent randomly heterogeneous medium. Our objective is to understand how the scintillation index of the measured…
We give an exact application of a recently developed, operator-based theory of wave propagation in dispersive, time-varying media. Using this theory we find that the usual symmetry of complex conjugation plus changing the sign of the…
It is shown that the commonly accepted definition for the Casimir scalar operators of the Poincare group does not satisfy the properties of Casimir invariance when applied to the non-inertial motion of elementary particles while in the…
Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schr\"odinger equations with potentials and nonlinearities depending on time and on the spatial coordinates. We present the general theory and use it…