Related papers: An explicit solution for deep water waves with Cor…
Recently a simple solution of the vacuum Einstein-Maxwell field equations was given describing a plane electromagnetic shock wave sharing its wave front with a plane gravitational impulse wave. We present here an exact solution of the…
Assuming that a formal approximation of multiple waves has been obtained by matched asymptotic methods, we derive a {\em Spatial Shadowing lemma} to construct exact solutions near the formal approximation. In Part I, we consider a general…
We present explicit solutions for the ordinary differential equations system describing the motion of the particles beneath small-amplitude capillary-gravity waves which propagate on the surface of an irrotational water flow with a flat…
A quasi-spherical approximation scheme, intended to apply to coalescing black holes, allows the waveforms of gravitational radiation to be computed by integrating ordinary differential equations.
This paper is devoted to the study of the long wave approximation for water waves under the influence of the gravity and a Coriolis forcing. We start by deriving a generalization of the Boussinesq equations in 1D (in space) and we…
We revisit and present new linear spaces of explicit solutions to incompressible Euler and Navier-Stokes equations on $\mathbb{R}^n$, as well as the rotating Boussinesq equations on $\mathbb{R}^3$. We cast these solutions are superpositions…
The future detection projects of gravitational waves are expected to have the sensitivity of detecting the primordial gravitational waves, which may be useful to get new insight into the very early universe. It is essential to analyze the…
Exact solutions of Einstein's vacuum equations are considered which describe gravitational waves with distinct wavefronts. A family of such solutions presented recently in which the wavefronts have various geometries and which propagate…
We determine the phase portrait of a Hamiltonian system of equations describing the motion of the particles in linear deep-water waves. The particles experience in each period a forward drift which decreases with greater depth.
We analyse the response of laser interferometric gravitational wave detectors using the full Maxwell equations in curved spacetime in the presence of weak gravitational waves. Existence and uniqueness of solutions is ensured by setting up a…
The Landau-Lifshitz form of the Lorentz-Abraham-Dirac equation in the presence of a plane wave of arbitrary shape and polarization is solved exactly and in closed form. The explicit solution is presented in the particular, paradigmatic…
It is well-known that the existence of traveling wave solutions for reaction-diffusion partial differential equations can be proved by showing the existence of certain heteroclinic orbits for related autonomous planar differential…
Analytical solutions to the wave equation in spheroidal coordinates in the short wavelength limit are considered. The asymptotic solutions for the radial function are significantly simplified, allowing scalar spheroidal wave functions to be…
In this paper we construct a new solution which represents Pollard-like three-dimensional nonlinear geophysical internal water waves. The Pollard-like solution includes the effects of the rotation of Earth and describes the internal water…
We show how Geophysics may illustrate and thus improve classical Mechanics lectures concerning the study of Coriolis force effects. We are then interested in atmospheric as well as oceanic phenomena we are familiar with, and are for that…
We give an explicit solution describing internal waves with a still water surface, modelling the dead water phenomenon, on the basis of the Gerstner wave solution to the Euler equations.
In order to improve the frequency dispersion effects of irrotational shallow water models in coastal oceanography, several full dispersion versions of classical models were formally derived in the literature. The idea, coming from G.…
We consider an asymptotic 1D (in space) rotation-Camassa-Holm (R-CH) model, which could be used to describe the propagation of long-crested shallow-water waves in the equatorial ocean regions with allowance for the weak Coriolis effect due…
This paper deals with the exact solutions of a nonlinear coupled coupled wave equation. The (G'/G)-expansion method has been applied to derive kink solutions and singular wave solutions. The restrictions on the coefficients of the governing…
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…