Related papers: Exact Pollard-like internal water waves
We present a brief discussion on the nonlinear Schr{\"o}dinger equation for modeling the propagation of the deep-water wavetrains and a discussion on its doubly-localized breather solutions that can be connected to the sudden formation of…
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…
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…
This article is concerned with an oceanographic model describing the asymptotic behaviour of a rapidly rotating and incompressible fluid with an inhomogeneous rotation vector; the motion takes place in a thin layer. We first exhibit a…
The collective dynamics of nonlinear electron waves in an one-dimensional degenerate electron gas is treated using the Lagrangian fluid approach. A new class of solutions with a nontrivial space and time dependence is derived. Both…
This paper is concerned with the global stability of the plane wave solutions to the relativistic string equation with non-small perturbations. Under certain decay assumptions on the plane wave, we conclude that the perturbed system admits…
The nonlinear propagation of internal gravity waves in the weakly ionized, incompressible Earth's ionosphere is studied using the fluid theory approach. Previous theory in the literature is advanced by the effects of the terrestrial…
Recent measurements at RHIC suggest that a nearly perfect fluid of quarks and gluons is produced in AA collisions. Moreover the passage of supersonic partons through this medium seems to produce waves. These waves might pile up and form…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…
Triad resonances for gravity waves propagating in opposite direction with respect to uniform current are introduced. They are produced by multivalued and anisotropic dispersion and occur even in deep water. In contrast, existing literature…
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…
The two-dimensional propagation of small-amplitude waves through an infinite periodic array of freely-floating rectangular floes is considered under the assumptions of inviscid linearised wave theory. Fluid gaps between adjacent floes allow…
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…
In this paper, we study the three-dimensional gravity-capillary water wave problem involving an irrotational, perfect fluid with gravity and surface tension. We focus on steady waves propagating uniformly in one direction. Assuming constant…
Solutions analogous to the Weber-Wheeler cylindrical pulse waves are found for the case of cylindrical gravitational waves in an expanding universe. These pulse solutions mimic the asymptotic properties of waves from an isolated source in…
A new method of solution is proposed for solution of the wave equation in one space dimension with continuously-varying coefficients. By considering all paths along which information arrives at a given point, the solution is expressed as an…
Starting from the classical formulation of the weak turbulence theory in a density stratified fluid, we derive a simplified version of the kinetic equation of internal gravity wave turbulence. This equation allows us to uncover scaling laws…
Two-dimensional periodic surface waves propagating under the combined influence of gravity and surface tension on water of finite depth are considered. Within the framework of small-amplitude waves, we find the exact solutions of the…
We consider small amplitude wave packet-like solutions to the 3D inviscid incompressible irrotational infinite depth water wave problem neglecting surface tension. Formal multiscale calculations suggest that the modulation of such a…
Long-distance transmission of energy by waves is a key mechanism for many natural processes. It becomes possible when the inhomogeneous medium is arranged in such a manner that it enables a specific type of waves to propagate with virtually…