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We consider three-dimensional geophysical flows at arbitrary latitude and with constant vorticity beneath a wave train and above a flat bed in the $\beta$-plane approximation with centripetal forces. We consider the $f$-plane approximation…
The signum-Gordon model in 1+1 dimensions possesses the exact shockwave solution with discontinuity of the field at the light cone and infinite gradient energy. The energy of a regular part of the wave inside the light cone is finite and it…
The mixed state of type II superconductors has magnetic flux penetrating the sample in the form of vortices, with each vortex carrying an identical quantum of flux. These vortices generally form a triangular lattice under weak mutually…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
We numerically simulate the two-dimensional inertial flow with the van der Waals effect in a straight periodic channel around the Poiseuille and Couette stationary states. Even though the flow remains laminar macroscopically, we observe…
We predict the existence of spatial-spectral vortex solitons in one-dimensional periodic waveguide arrays with quadratic nonlinear response. In such vortices the energy flow forms a closed loop through the simultaneous effects of phase…
Strong lensing by intervening galaxies can produce multiple images of gravitational waves from sources at cosmological distances. These images acquire additional phase-shifts as the over-focused wavefront passes through itself along the…
We study interaction of inertial waves with geostrophic flow in a rapidly rotating fluid system. In accordance with experimental conditions in [1, 2], we consider inertial waves, which were excited by a source being near side boundary of…
The weakly nonlinear dynamics of the free surface of a dielectric liquid in an electric field directed tangentially to the unperturbed boundary is investigated numerically. Within the framework of the strong field model, when the effects of…
Wave-like spatial statistics in walking-droplet quantum analogs are typically attributed to spatial or temporal nonlocal wave effects. We show instead that such behavior arises generically from the low-dimensional nonlinear dynamics of an…
We investigate a new property of retarded Green's functions using AdS/CFT. The Green's functions are not unique at special points in complex momentum space. This arises because there is no unique incoming mode at the horizon and is similar…
Numerical simulation has indicated that vortex structures can exist for a long time in the form of quantized filaments on arrays of coupled weakly dissipative nonlinear oscillators in a finite three-dimensional domain under a resonant…
We develop a theory of turbulence of weak random gravity waves on surface of deep water in which the main nonlinear process at high-frequency part of the spectrum is a nonlocal interaction with a strong low-frequency component. The latter…
We introduce a novel type of surface waves that form at the edge of guiding structures consisting of several concentric rings. Such surface waves rotate steadily upon propagation and, in contrast to nonrotating waves, for high rotation…
The turbulence of capillary waves on the surface of a ferrofluid with a high permeability in a horizontal magnetic field is considered in the framework of a one-dimensional weakly nonlinear model. In the limit of a strong magnetic field,…
This paper concerns the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating slab (between two parallel planes) in the weak-scattering regime, and the study of boundary effects through an…
We report high-resolution measurements of three-dimensional (3D) turbulence in a rapidly rotating fluid. By decomposing the velocity field into a vertically averaged component and a three-dimensional residual, we show that each dominates…
We consider time-harmonic incompressible flow with a spatially resolved complex viscosity field $\mu^*(\mathbf{x},\omega)$ and, at fixed forcing frequency $\omega>0$, its constitutive phase texture…
An interface between two media is topologically stable two-dimensional object where 3D-symmetry breaks which allows for existence of many exotic excitations. A direct way to explore surface excitations is to investigate their interaction…
Vortex flows can foster a variety of wave modes. A recent oscillatory analysis of a persistent 1.7 h vortex flow with a significant substructure has suggested the existence of various types of waves within it. We investigate the nature and…