Related papers: On multisolitonic decay behavior of internal gravi…
This paper considers the existence and stability properties of two-dimensional solitary waves traversing an infinitely deep body of water. We assume that above the water is vacuum, and that the waves are acted upon by gravity with surface…
This article concerns the Cauchy problem for the gravity-capillary water waves system in general dimensions. We establish local well-posedness for initial data in $H^s$, with $s > \frac{d}{2} + 2 - \mu$, with $\mu = \frac{3}{14}$ and $\mu =…
This is the second and last paper of a series aimed at solving the local Cauchy problem for polarized $\mathbb U(1)$ symmetric solutions to the Einstein vacuum equations featuring the nonlinear interaction of three small amplitude impulsive…
The Euler's equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymtotic expansion of the Euler's equations is taken (to a certain order of smallness of the scale parameters), relations to…
The following development of the well-known "vertical modes and horizontal rays" approach for acoustic waves propagation in shallow water, introduced in different works, is studied. In this approach we study so-called space-time horizontal…
The Cauchy problem for harmonic maps from Minkowski space with its standard flat metric to a certain non-constant curvature Lorentzian 2-metric is studied. The target manifold is distinguished by the fact that the Euler-Lagrange equation…
An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting…
The flow field of a bluff body, a circular disk, that moves horizontally in a stratified environment is studied using large eddy simulations (LES). Five levels of stratification (body Froude numbers of Fr = 0.5, 1, 1.5, 2 and 5) are…
A numerical method is developed to study the stability of standing water waves and other time-periodic solutions of the free-surface Euler equations using Floquet theory. A Fourier truncation of the monodromy operator is computed by solving…
The dynamics of internal waves in stratified media, such as the ocean or atmosphere, is highly dependent on the topography of their floor. A closed-form analytical solution can be derived only in cases when the water distribution density…
The cosmological constant induced by quantum fluctuation of the graviton on a given background is considered as a tool for building a spectrum of different geometries. In particular, we apply the method to the Schwarzschild background with…
The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical…
We study numerically the Cauchy problem for equivariant wave maps from 3+1 Minkowski spacetime into the 3-sphere. On the basis of numerical evidence combined with stability analysis of self-similar solutions we formulate two conjectures.…
We consider the asymptotic behaviour of small-amplitude gravity water waves in a rectangular domain where the water depth is much smaller than the horizontal scale. The control acts on one lateral boundary, by imposing the horizontal…
Two-dimensional nonlinear gravity waves travelling in shallow water on a vertically sheared current of constant vorticity are considered. Using Euler equations, in the shallow water approximation, hyperbolic equations for the surface…
The dynamics of solitary gravity-capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time dependent solutions, we simplify the full potential…
In this paper we study the motion of an internal water wave and an internal wave in a porous medium. For these problems we establish that, if the free boundary and, in the case of the Euler equations, also the tangential velocity at the…
In this contribution we describe the role of several two-component integrable systems in the classical problem of shallow water waves. The starting point in our derivation is the Euler equation for an incompressible fluid, the equation of…
This paper presents a new numerical model based on the highly nonlinear potential flow theory for simulating the propagation of water waves in variable depth. A new set of equations for estimating the surface vertical velocity is derived…
A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision. The method is used to study resonance and its effect on…