Related papers: Exact solutions for small-amplitude capillary-grav…
A fifth--order nonlinear partial differential equation for the description of nonlinear waves in a liquid with gas bubbles is considered. Special solutions of this equation are studied. Some elliptic and simple periodic traveling waves…
This paper establishes the conditional orbital stability of fully localized solitary waves for the three-dimensional capillary-gravity water wave problem in finite depth under strong surface tension. The waves, constructed via a…
We investigate steady symmetric gravity water waves on finite depth. For non-positive vorticity it is shown that the particles display a mean forward drift, and for a class of waves we prove that the size of this drift is strictly…
We prove the first bifurcation result of time quasi-periodic traveling waves solutions for space periodic water waves with vorticity. In particular we prove existence of small amplitude time quasi-periodic solutions of the gravity-capillary…
For propagation of surface shallow-water waves on irrotational flows, we derive a new two-component system. The system is obtained by a variational approach in the Lagrangian formalism. The system has a non-canonical Hamiltonian…
In this paper we construct small amplitude periodic internal waves traveling at the boundary region between two rotational and homogeneous fluids with different densities. Within a period, the waves we obtain have the property that the…
A fundamental non-classical fourth-order partial differential equation to describe small amplitude linear oscillations in a rotating compressible fluid, is obtained. The dispersion relations for such a fluid, and the different regions of…
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…
We consider the gravity-capillary water waves equations of a 2D fluid with constant vorticity. By employing variational methods we prove the bifurcation of periodic traveling water waves -- which are steady in a moving frame -- for {\it…
We prove that the 2D finite depth capillary water wave equations admit no solitary wave solutions. This closes the existence/non-existence problem for solitary water waves in 2D, under the classical assumptions of incompressibility and…
The magnetohydrodynamic equations system for heavy fluid over an arbitrary surface in shallow water approximation is studied in the present paper. It is shown that simple wave solutions exist only for underlying surfaces that are slopes of…
We present the derivation of generic equations describing the long gravity waves in incompressible fluid with decaying effect. We show that in this theory the only restriction to the surface deviation is connected with the stability…
This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…
We consider steady three-dimensional gravity-capillary water waves with vorticity propagating on water of finite depth. We prove a variational principle for doubly periodic waves with relative velocities given by Beltrami vector fields,…
We construct small amplitude gravity-capillary water waves with small nonzero vorticity, in three spatial dimensions, bifurcating from uniform flows. The waves are symmetric, and periodic in both horizontal coordinates. The proof is…
The propagation of water waves of finite depth and flat bottom is studied in the case when the depth is not small in comparison to the wavelength. This propagation regime is complementary to the long-wave regime described by the famous KdV…
We use Clebsch potentials and an action principle to derive a closed system of gauge invariant equations for sound superposed on a general background flow. Our system reduces to the Unruh (1981) and Pierce (1990) wave equations when the…
When traditional linearised theory is used to study gravity-capillary waves produced by flow past an obstruction, the geometry of the object is assumed to be small in one or several of its dimensions. In order to preserve the nonlinear…
This article is concerned with the incompressible, irrotational infinite depth water wave equation in two space dimensions, without gravity but with surface tension. We consider this problem expressed in position-velocity potential…
Light waves carry along their own gravitational field; for simple plain electromagnetic waves the gravitational field takes the form of a pp-wave. I present the corresponding exact solution of the Einstein-Maxwell equations and discuss the…