Related papers: Numerical simulation of oscillatons: extracting th…
This paper investigates wave-equations on spacetimes with a metric which is locally analytic in the time. We use recent results in the theory of the non-characteristic Cauchy problem to show that a solution to a wave-equation vanishing in…
We study an ensembles of globally coupled or forced identical phase oscillators subject to independent white Cauchy noise. We demonstrate, that if the oscillators are forced in several harmonics, stationary synchronous regimes can be…
We study the quantum properties of an oscillator in proper time. This proper time oscillator is a particle model with mass that is on shell. Its internal time can be treated as a self-adjoint operator. The displaced time and displaced time…
In Class. Quantum Grav. 26 (2009) 175006 (arXiv:0812.4333v3) Bizon et al discuss the power-law tail in the long-time evolution of a spherically symmetric self-gravitating massless scalar field in odd spatial dimensions. They derive explicit…
We find vacuum solutions such that massive gravitons are confined in a local spacetime region by their gravitational energy in asymptotically flat spacetimes in the context of the bigravity theory. We call such self-gravitating objects…
We solve the fifth-order Korteweg-de Vries (fKdV) equation which is a modified KdV equation perturbed by a fifth-order derivative term multiplied by a small parameter $\epsilon^2$, with $0< \epsilon \ll 1$. Unlike the KdV equation, the…
In this paper, we consider the perturbed solutions with polynomial tail in large velocities for the non-cutoff Boltzmann equation near global Maxwellians in the whole space. The global in time existence is proved in the weighted Sobolev…
We initiate the study of the asymptotic behavior of small solutions to one-dimensional Klein-Gordon equations with variable coefficient quadratic nonlinearities. The main discovery in this work is a striking resonant interaction between…
We consider spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant in five dimensions and analyze evolution of small perturbations of anti-de Sitter spacetime using the recently proposed resonant…
The dynamics of qubits coupled to a harmonic oscillator with time-periodic coupling is investigated in the framework of Floquet theory. This system can be used to model nonadiabatic phenomena that require a periodic modulation of the…
We study the Cauchy problem for a system of cubic nonlinear Klein-Gordon equations in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the solution exists globally and decays of the order…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
The possibility has been recently demonstrated to manufacture (nonrelativistic, Hamiltonian) many-body problems which feature an isochronous time evolution with an arbitrarily assigned period $T$ yet mimic with good approximation, or even…
In this work we study a nonlinear Volterra equation with non-symmetric feedback that arises as a particular case of the Gurtin-MacCamy model in population dynamics. We are particularly interested in the existence of slowly oscillating…
We study the influence of the friction term on the radially symmetric solutions of the repulsive Euler-Poisson equations with a non-zero background, corresponding to cold plasma oscillations in many spatial dimensions. It is shown that for…
We consider radial solutions to the Schr\"odinger-Poisson system in three dimensions with an external smooth potential with Coulomb-like decay. Such a system can be viewed as a model for the interaction of dark matter with a bright matter…
It is shown by both analytical methods and numerical simulations that extremely long living spherically symmetric oscillons appear in virtually any real scalar field theory coupled to a massless dilaton (DS theories). In fact such…
This paper presents a comprehensive analysis of several aspects of the sinh-Gordon equation within a periodic setting. Our investigation proceeds in three main stages. First we establish the existence of periodic solutions for a fixed wave…
We study the asymptotic behavior and the scattering from infinity problem for the massive Maxwell-Klein-Gordon system in the Lorenz gauge, which were previously only studied for the massless system. For a general class of initial data, in…
We study {\it analytically} the characteristic resonance spectrum of charged massive scalar fields linearly coupled to a spherically symmetric charged reflecting shell. In particular, we use analytical techniques in order to solve the…