Related papers: Two- and Three-dimensional Generalisation of Lower…
To resolve some unphysical interpretations related to velocity measurements by static observers, we discuss the use of generalized observer sets, give a prescription for defining the speed of test particles relative to those observers and…
We investigate the existence of solitary gravity waves traversing a two-dimensional body of water that is bounded below by a flat impenetrable ocean bed and above by a free surface of constant pressure. Our main interest is constructing…
For semi-linear wave equations with null form non-linearities on $\mathbb{R}^{3+1}$, we exhibit an open set of initial data which are allowed to be large in energy spaces, yet we can still obtain global solutions in the future. We also…
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…
Generic wave dislocations (phase singularities, optical vortices) in three dimensions have anisotropic local structure, which is analysed, with emphasis on the twist of surfaces of equal phase along the singular line, and the rotation of…
A gauge-invariant formulation for the gravitational wave equations is presented. Using this approach, weak, plane wave solutions in a vacuum are derived in various theories. These include general relativity with two modes of polarization…
In this work an extended elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate to classify new exact travelling wave solutions expressible in terms of quasi-periodic…
We present a general theory of three-dimensional nonparaxial spatially-accelerating waves of the Maxwell equations. These waves constitute a two-dimensional structure exhibiting shape-invariant propagation along semicircular trajectories.…
In the FIRST PART we present simple introductions to gaussian and Bessel waves, and to the Localized Waves (LW), pulses or beams, showing the important properties of the latter, and their applications whenever a role is played by a…
We construct three-dimensional families of small-amplitude gravity-driven rotational steady water waves on finite depth. The solutions contain counter-currents and multiple crests in each minimal period. Each such wave generically is a…
We consider spatially coupled systems governed by a set of scalar density evolution equations. Such equations track the behavior of message-passing algorithms used, for example, in coding, sparse sensing, or constraint-satisfaction…
This article is concerned with infinite depth gravity water waves in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. Our goal is to study this problem with small wave packet…
In this paper we consider two-dimensional water waves with constant vorticity, under the action of gravity and surface tension, in a fluid domain with finite depth and general bottom topography. We present a formulation which generalizes…
The measurement of distance between two objects is generalized to the case where the objects are no longer points but are one-dimensional. Additional concepts such as non-extensibility, curvature constraints, and non-crossing become central…
All random wave fields possess a network of phase singularities. We show that while the phase statistics within speckle patterns is generic, the statistics of the motion of phase singularities differs substantially for diffusive and…
We compute the distribution of relative velocities for a one-dimensional model of heavy particles suspended in a turbulent flow, quantifying the caustic contribution to the moments of relative velocities. The same principles determine the…
A new description for highly nonlinear potential water waves is suggested, where weak 3D effects are included as small corrections to exact 2D equations written in conformal variables. Contrary to the traditional approach, a small parameter…
We calculate certain estimates for the solution of the characteristic problem of the wave equation reduced to first order, in terms of the free data prescribed on two transverse surfaces, one of which is characteristic. Estimates of such…
We prove the existence of small solitary waves for one-dimensional lattices of particles that each repel every other particle with a force that decays as a power of distance. For force exponents $\alpha+1$ with $\frac43<\alpha<3$, we employ…
Wave vortices constitute a large family of wave entities, closely related to phase singularities and orbital angular momentum (OAM). So far, two main classes of localized wave vortices have been explored: (i) transversely-localized…