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We derive the perturbation equations for relativistic stars in scalar-tensor theories of gravity and study the corresponding oscillation spectrum. We show that the frequency of the emitted gravitational waves is shifted proportionally to…
We derive a manifestly duality-symmetric formulation of the action principle for conformal gravity linearized around Minkowski space-time. The analysis is performed in the Hamiltonian formulation, the fourth-order character of the equations…
A formalism is introduced which may describe both standard linearized waves and gravitational waves in Isaacson's high-frequency limit. After emphasizing main differences between the two approximation techniques we generalize the Isaacson…
The physical situation of the collision and subsequent interaction of plane gravitational waves in a Minkowski background gives rise to a well-posed characteristic initial value problem in which initial data are specified on the two null…
We consider two-dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and surface tension. The upper fluid is bounded above by a rigid lid, and the lower fluid is bounded below by a rigid bottom. We use a…
We present here a relativistic theory of gravity in which the spacetime metric is derived from a single scalar field $\Phi$. The field equation, derived from a simple variational principle, is a non-linear flat-space four-dimensional wave…
In this paper we investigate the gravitational waves emission by stellar dynamical structures as complex systems in the quadrupole approximation considering bounded and unbounded orbits. Precisely, after deriving analytical expressions for…
Recently Harada has proposed a gravitational theory which is of third order in the derivatives of the metric tensor. This has attracted some attention particularly as it predicts a late-time transition from cosmological decelaration to…
The Petviashvili's iteration method has been known as a rapidly converging numerical algorithm for obtaining fundamental solitary wave solutions of stationary scalar nonlinear wave equations with power-law nonlinearity: \ $-Mu+u^p=0$, where…
Gravitational waves at suitable frequencies can resonantly interact with a binary system, inducing changes to its orbit. A stochastic gravitational-wave background causes the orbital elements of the binary to execute a classic random walk,…
We compute the instantaneous contributions to the spherical harmonic modes of gravitational waveforms from compact binary systems in general orbits up to the third post-Newtonian order. We further extend these results for compact binaries…
In this paper we use a traveling wave reduction or a so-called spatial approximation to comprehensively investigate the periodic solutions of the complex cubic-quintic Ginzburg-Landau equation. The primary tools used here are Hopf…
The Einstein equations for a plane-symmetric gravitational field coupled to an arbitrary nonlinear sigma model (NSM) are shown to be represented in the form of dynamical equations of a {\it generalized effective NSM}. The gravitational…
The inclusion of stochastic terms in equations of motion for fluid problems enables a statistical representation of processes which are left unresolved by numerical computation. Here, we derive stochastic equations for the behaviour of…
Following a recent proposal to describe inelastic eikonal scattering processes in terms of gravitationally dressed elastic eikonal amplitudes, we motivate a collinear double graviton dressing and investigate its properties. This is derived…
To clarify certain nonlinear properties of strong gravitational field, we investigate cylindrically symmetric gravitational waves that are localized as regular wave packets in the space of radial and time coordinates. The waves are…
Solutions of the system of evolutionary equations in the short-wavelength approximation are found and studied. A connection is established between the problem of the evolution of short-wavelength gravitational-scalar perturbations and the…
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 travelling-wave spatially periodic solutions of a forced Cahn-Hilliard equation. This is a model for phase separation of a binary mixture, subject to external forcing. We look at arbitrary values of the mean mixture concentration,…
This paper is devoted to the study of periodic solutions for a radially symmetric semilinear wave equation in an $n$-dimensional ball. By combining the variational methods and saddle point reduction technique, we prove there exist at least…