Related papers: Linear Stability Analysis of Dynamical Quadratic G…
We review asymptotic stability of solitary waves for nonlinear dispersive equations set on the line. Our focus is threefold: first, the nonlinear Schrodinger equation; second, the notion of full asymptotic stability (which states that…
The stability of a rotating fluid disk to the formation of spiral arms is studied in the tightwinding approximation in the linear regime. The dispersion relation for spirals that was derived by Bertin et al. is shown to contain a new,…
We apply spectral stability theory to investigate nonlinear gravity waves in the atmosphere. These waves are determined by modulation equations that result from Wentzel-Kramers-Brillouin theory. First, we establish that plane waves, which…
We study stability of the Dynamical Fixed Points (DFPs) of the cascading gauge theory at strong coupling in de Sitter space-time. We compute the spectra of the perturbative fluctuations and identify stable/unstable DFPs, characterized by…
We investigate a non-perturbative approach to quantum gravity built in terms of analogies between quadratic gravity and quantum chromodynamics. This approach is based on a conjectured phase transition between quadratic gravity in the…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…
This study explores the gravitational collapse of a massless scalar field within Quadratic Gravity treated as a dimension-four operator Effective Field Theory extension to General Relativity. The additional degrees of freedom associated…
In this paper, the emission of gravitational waves in quadratic gravity theory is examined. The wave equations for massless and massive perturbations are derived, followed by the calculation of the energy and angular momentum radiated. In…
Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are…
We study the cosmological perturbations of the recently proposed extension of non-linear massive gravity with a scalar field. The added scalar field ensures a new symmetry on the field space of the theory. The theory has the property of…
This paper is devoted to study the stability/instability of the expansionfree self gravitating source in the framework of Einstein Gauss-Bonnet gravity. The source has been taken as Tolman-Bondi model which is homogenous in nature. The…
Two accelerating cosmological models are presented in symmetric teleparallel $f(Q)$ gravity, $Q$ be the non-metricity. The models are constructed based on the assumptions of two different functional forms of $f(Q)$ and a dynamically…
A discussion of the number of degrees of freedom, and their dynamical properties, in higher derivative gravitational theories is presented. The complete non-linear sigma model for these degrees of freedom is exhibited using the method of…
The dynamics of metric perturbations is explored in the gravity theory with anomaly-induced quantum corrections. Our first purpose is to derive the equation for gravitational waves in this theory on the general homogeneous and isotropic…
We study the stability of the dynamics of a network of n neurons intercting linearly through a random gaussian matrix of excitatory and inhibitory type. Using the aproach developed in a previous paper we show some interesting properties of…
We perform a space-time analysis of the D>4 quadratic curvature Lanczos-Lovelock (LL) model, exhibiting its dependence on intrinsic/extrinsic curvatures, lapse and shifts. As expected from general covariance, the field equations include D…
We study transmission stabilization of optical solitons against emission of radiation in nonlinear optical waveguides in the presence of weak linear gain-loss, cubic loss, and the collisional Raman frequency shift. We first show how the…
The so-called ``symplectic method'' is used for studying the linear stability of a self-gravitating collisionless stellar system, in which the particles are also submitted to an external potential. The system is steady and spherically…
Transmission through a complex network of nonlinear one-dimensional leads is discussed by extending the stationary scattering theory on quantum graphs to the nonlinear regime. We show that the existence of cycles inside the graph leads to a…
We are concerned with the dynamical behavior of solutions to semilinear wave systems with time-varying damping and nonconvex force potential. Our result shows that the dynamical behavior of solution is asymptotically stable without any…