Related papers: Efficient formulation of the periodic corrections …

We address Euler's equations for irrotational gravity waves in an infinitely deep fluid rewritten in conformal variables. Stokes waves are traveling waves with the smooth periodic profile. In agreement with the previous numerical results,…

The aim of this paper is to find higher order geometrical corrections to the Einstein-Hilbert action that can lead to only second order equations of motion. The metric formalism is used, and static spherically symmetric and…

The modified theories of gravity, especially the $f(R)$ gravity, have attracted much attention in the last decade. This paper is devoted to exploring plane symmetric solutions in the context of metric $f(R)$ gravity. We extend the work on…

Spinor gravity is a functional integral formulation of gravity based only on fundamental spinor fields. The vielbein and metric arise as composite objects. Due to the lack of local Lorentz-symmetry new invariants in the effective…

The real, nonsingular elliptic solutions of the Korteweg-deVries equation are studied through the time dynamics of their poles in the complex plane. The dynamics of these poles is governed by a dynamical system with a constraint. This…

We present new exact solutions of the warped spherical compactifications in the higher-dimensional gravitational theory coupled to scalar and several form field strengths. We find two classes of solutions. One has a de Sitter spacetime with…

We derive the effects of a non-zero cosmological constant $\Lambda$ on gravitational wave propagation in the linearized approximation of general relativity. In this approximation we consider the situation where the metric can be written as…

We consider the Maxwell-Bloch system which is a finite-dimensional approximation of the coupled nonlinear Maxwell-Schr\"odinger equations. The approximation consists of one-mode Maxwell field coupled to two-level molecule. We construct…

In Einstein's theory of relativity, the interaction of two collinearly polarized plane gravitational waves can be described by a Goursat problem for the Euler--Darboux equation in a triangular domain. In this paper, using a representation…

Equilibria of binary neutron stars in close circular orbits are computed numerically in a waveless formulation: The full Einstein-relativistic-Euler system is solved on an initial hypersurface to obtain an asymptotically flat form of the…

The Boltzmann equation without an angular cutoff is considered when the initial data is a small perturbation of a global Maxwellian with an algebraic decay in the velocity variable. A well-posedness theory in the perturbative framework is…

We investigate a model of inflationary cosmology where the minimally coupled scalar field theory is modified by additional correction terms. Among the most general ten correction terms remarked by Weinberg in context of effective field…

Simple form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback…

Motivated by statements in the literature which contradict two general theorems, the static and spherically symmetric Brans solutions of scalar-tensor gravity are analyzed explicitly in both the Jordan and the Einstein conformal frames.…

We discuss how to extract information about the cosmological constant from the Wheeler-DeWitt equation, considered as an eigenvalue of a Sturm-Liouville problem. A generalization to a f(R)theory is taken under examination. The equation is…

We investigate the cosmological dynamics of nonlocally corrected gravity involving a function of the inverse d'Alembertian acting on the Gauss-Bonnet term. Casting the dynamical equations in local form, we derive the reconstruction…

In the present paper, we discuss gravitational relaxation models for the electroweak hierarchy problem. We show that modified gravity can naturally relax the electroweak hierarchy problem where conformal transformation provides a crucial…

We discuss the existence of inflationary solutions in a class of renormalization group improved polynomial f(R) theories, which have been studied recently in the context of the asymptotic safety scenario for quantum gravity. These theories…

We consider the initial-value problem for the regularized Boussinesq-Ostrovsky equation in the class of periodic functions. Validity of the weakly-nonlinear solution, given in terms of two counter-propagating waves satisfying the uncoupled…

We consider a model for gravity that is invariant under global scale transformations. It includes one extra real scalar field coupled non-minimally to the gravity fields. In this model all the dimensionful parameters like the gravitational…