Related papers: Two- and Three-dimensional Generalisation of Lower…
The classical far field concept of wave velocities has its merits while exibiting intrinsic difficulties. A general local approach for the definition of velocities and especially phase velocities for waves avoiding these difficulties is…
The classical characterization of \wp, as a typical concept for far field phenomena, has been successfully applied to many \w phenomena in past decades. The recent reports of superluminal tunnelling times and negative group velocities…
Wave localization is a ubiquitous phenomenon. It refers to situations that transmitted waves in scattering media are trapped in space and remain confined in the vicinity of the initial site until dissipated. Based on a scaling analysis, the…
The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…
This article is concerned with the infinite depth water wave equation in two space dimensions. We consider this problem expressed in position-velocity potential holomorphic coordinates,and prove that small localized data leads to global…
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…
It is proposed to apply a recently developed concept of local wave velocities to the dynamical field characteristics, especially for the canonical field energy density. It is shown that local energy velocities can be derived from the…
It has been the dominant view for over two decades that all waves are localized in two dimensions for any given amount of disorder. Here, I would like to raise questions about this assertion. The discussion leads to the conclusion that…
This paper studies the structural implications of constant vorticity for steady three-dimensional internal water waves. It is known that in many physical regimes, water waves beneath vacuum that have constant vorticity are necessarily two…
Fully localised solitary waves are travelling-wave solutions of the three-dimensional gravity-capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence for water of finite depth has recently…
The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows which are families of probability distributions on the space of solutions to the associated ODEs, which no longer satisfy…
Local time is the measure of how much time a random walk has visited a given position. In multiple scattering media, where waves are diffuse, local time measures the sensitivity of the waves to the local medium's properties. Local…
Motivated by previous investigations on the radiative effects of the electric dipoles embedded in structured cavities, localization of electromagnetic waves in two dimensions is studied {\it ab initio} for a system consisting of many…
We give a new, wave-like solution of the field equations of five-dimensional relativity. In ordinary three-dimensional space, the waves resemble de Broglie or matter waves, whose puzzling behaviour can be better understood in terms of one…
A general type of localized excitations, folded solitary waves and foldons, are defined and studied both analytically and graphically. The folded solitary waves and foldons may be "folded" in quite complicated ways and possess quite rich…
This short note is about the gauge condition for the velocity potential, the definitions of the Bernoulli constant and of the velocity speeds in the context of water waves. These definitions are often implicit and thus the source of…
We study the two-dimensional gravity water waves with a one-dimensional interface with small initial data. Our main contributions include the development of two novel localization lemmas and a Transition-of-Derivatives method, which enable…
This article represents the second installment of a series of papers concerned with low regularity solutions for the water wave equations in two space dimensions. Our focus here is on global solutions for small and localized data. Such…
We prove Strichartz estimates for gravity water waves, in arbitrary dimension and in fluid domains with general bottoms. We consider rough solutions such that, initially, the first order derivatives of the velocity field are not controlled…
We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L^2 related norms, with dispersive estimates, which give decay…