Related papers: Boson Stars with Long-range Perturbations
A simple model to study boson stars is to consider these stellar objects as quantum systems of $N$ identical self-gravitating particles within a non-relativistic framework. Some results obtained with point-like particles are recalled as…
We investigate boson stars in an $O(3)$ scalar field theory with a symmetry-breaking potential. By constructing numerically spherically symmetric solutions, we demonstrate that the model gives rise to a rich set of field configurations. The…
We consider the nonlinear Schr{\"o}dinger equation (NLSE) in 1+1 dimension with scalar-scalar self interaction $\frac{g^2}{\kappa+1} (\psi^\star \psi)^{\kappa+1}$ in the presence of the external forcing terms of the form $r e^{-i(kx +…
We consider (2+1)-dimensional beams, whose transverse size may be comparable to or smaller than the carrier wavelength, on the basis of an extended version of the nonlinear Schr\"{o}dinger equation derived from the Maxwell`s equations. As…
In this paper, we study the existence and instability of standing waves with a prescribed $L^2$-norm for the fractional Schr\"{o}dinger equation \begin{equation} i\partial_{t}\psi=(-\Delta)^{s}\psi-f(\psi), \qquad (0.1)\end{equation} where…
In this paper we propose a notion of stability, that we call $\epsilon -N$-stability, for systems of particles interacting via Newton's gravitational potential, and orbiting a much bigger object. For these systems the usual thermodynamical…
We perform numerical evolutions of the fully non-linear Einstein-(complex, massive)Klein-Gordon and Einstein-(complex)Proca systems, to assess the formation and stability of spinning bosonic stars. In the scalar/vector case these are known…
The paper discusses nonlinear singular perturbations of delta type of the fractional Schr\"odinger equation $\imath\partial_t\psi=\left(-\triangle\right)^s\psi$, with $s\in(\frac{1}{2},1]$, in dimension one. Precisely, we investigate local…
We analyse systematically, from the viewpoint of the nonlinear physics of solitary waves, the effect of the spatial dimension (D = 1,2,3) on the structure and stability of the Bose-Einstein condensates (BECs) trapped in an external…
Axions and axion-like particles are a leading model for the dark matter in the Universe; therefore, dark matter halos may be boson stars in the process of collapsing. We examine a class of static boson stars with a non-minimal coupling to…
We consider the Schr{\"o}dinger equation with a nondispersive logarithmic nonlinearity and a repulsive harmonic potential. For a suitable range of the coefficients, there exist two positive stationary solutions, each one generating a…
We study strong instability of standing waves $e^{i\omega t} \phi_{\omega}(x)$ for nonlinear Schr\"odinger equations with $L^2$-supercritical nonlinearity and a harmonic potential, where $\phi_{\omega}$ is a ground state of the…
Starting from the spectrum of the radially symmetric quantum harmonic oscillator in two dimensions, we create a large set of nonlinear solutions. The relevant three principal branches, with $n_r=0,1$ and 2 radial nodes respectively, are…
We consider the focusing $L^2$-supercritical fractional nonlinear Schr\"odinger equation \[ i\partial_t u - (-\Delta)^s u = -|u|^\alpha u, \quad (t,x) \in \mathbb{R}^+ \times \mathbb{R}^d, \] where $d\geq 2, \frac{d}{2d-1} \leq s <1$ and…
We study the structure of neutron stars in R+\beta\ R^{\mu \nu} R_{\mu \nu} gravity model with perturbative method. We obtain mass--radius relations for six representative equations of state (EoSs). We find that, for |\beta| ~ 10^11 cm^2,…
There is increasing numerical evidence that scalar fields can form long-lived quasi-bound states around black holes. Recent perturbative and numerical relativity calculations have provided further confirmation in a variety of physical…
We consider the quantum Non-linear Schr\"{o}dinger equation $i\partial_t\Psi=-\partial_x^2\Psi +2c\Psi^\dagger\Psi^2$ with positive coupling constant $c$ varying from zero to infinity. We study quantum correlation functions of this model…
We consider a full set of harmonics for the Stokes wave in deep water in the absence of viscosity, and examine the role that higher harmonics play in modifying the classical Benjamin-Feir instability. Using a representation of the wave…
Vector boson stars, also known as Proca stars, exhibit remarkable dynamical robustness, making them strong candidates for potential astrophysical exotic compact objects. In search of theoretically well-motivated Proca star models, we…
We prove a general, non-perturbative result about finite-time blowup solutions for the $L^2$-critical boson star equation $i\partial_t u = \sqrt{-\Delta+m^2} \, u - (|x|^{-1} \ast |u|^2) u$ in 3 space dimensions. Under the sole assumption…