Related papers: Super compact equation for water waves
Using the Einstein gravitation theory we show how to obtain the basic equations which predict the gravitational waves. This paper was written to graduate and post-graduate students of Physics. We deduce the equations didactically following…
In this paper, we consider a wave equation with strong damping and logarithmic nonlinearity. This paper aims to study the local and global existence, uniqueness and the uniform energy decay rate of a weak solution under some sufficient…
Sufficient conditions for wave breaking are found for the short-pulse equation describing wave packets of few cycles on the ultra-short pulse scale. The analysis relies on the method of characteristics and conserved quantities of the…
We construct small-amplitude steady periodic gravity water waves arising as the free surface of water flows that contain stagnation points and possess a discontinuous distribution of vorticity in the sense that the flows consist of two…
Third-order nonlinear dispersion equations (NDEs) are shown to admit both shock and rarefaction waves (as weak solutions), which are distinguished by a smooth deformation approach. Compacton-type travelling wave solutions are proved to be…
A new operator equation for periodic gravity waves on water of finite depth is derived and investigated; it is equivalent to Babenko's equation considered in \cite{KD}. Both operators in the proposed equation are nonlinear and depend on the…
Lorentz violations in gravitational waves are investigated. Plane-wave solutions for arbitrary gauge-invariant violations in linearized gravity are constructed. Signatures of Lorentz violation include dispersion, birefringence, and…
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and…
This chapter gives an introduction to the connection between the physics of water waves and analogue gravity. Only a basic knowledge of fluid mechanics is assumed as a prerequisite.
It is shown that the dynamical evolution of linear perturbations on a static space-time is governed by a constrained wave equation for the extrinsic curvature tensor. The spatial part of the wave operator is manifestly elliptic and…
We study the axial gravitational perturbations of slowly-rotating compact objects which are assumed to be supported by anisotropic fluids. We find that the gravitational perturbations decouple from the matter perturbations for axial…
We write the equation of geodesic deviations in the spacetime of $pp$-waves in terms of the Newman-Penrose scalars and apply it to study gravitational waves in quadratic curvature gravity. We show that quadratic curvature gravity $pp$-waves…
For two-dimensional steady pure-gravity water waves with a unidirectional flow of constant favourable vorticity, we prove an explicit bound on the amplitude of the wave, which decays to zero as the vorticity tends to infinity. Notably, our…
We prove the nonexistence of two-dimensional solitary gravity water waves with subcritical wave speeds and an arbitrary distribution of vorticity. This is a longstanding open problem, and even in the irrotational case there are only partial…
We prove local exact controllability in arbitrary short time of the two-dimensional incompressible Euler equation with free surface, in the case with surface tension. This proves that one can generate arbitrary small amplitude periodic…
The relationship between pulsar-like compact stars and gravitational waves is briefly reviewed. Due to regular spins, pulsars could be useful tools for us to detect ~nano-Hz low-frequency gravitational waves by pulsar-timing array…
Internal waves describe the (linear) response of an incompressible stably stratified fluid to small perturbations. The inclination of their group velocity with respect to the vertical is completely determined by their frequency. Therefore…
Part A of this article is devoted to the general investigation of the gravitational-wave emission by post-Newtonian sources. We show how the radiation field far from the source, as well as its near-zone inner gravitational field, can (in…
In order to obtain quite precise information about the shape of the particle paths below small-amplitude gravity waves travelling on irrotational deep water, analytic solutions of the nonlinear differential equation system describing the…
Using Levi-Civita's theory of ideal fluids, we derive the complex Korteweg-de Vries (KdV) equation, describing the complex velocity of a shallow fluid up to first order. We use perturbation theory, and the long wave, slowly varying velocity…