Related papers: Instability of sphalerons in $\phi^4$ models with …
The Klein-Gordon equation for a scalar field sourced by a static spherically symmetric background is an interesting second-order differential equation with applications in particle physics, astrophysics, and elsewhere. Here we present…
We describe a new cooling algorithm for SU(2) lattice gauge theory. It has any critical point of the energy or action functional as a fixed point. In particular, any number of unstable modes may occur. We also provide insight in the…
We consider the instability and stability of periodic stationary solutions to the classical \phi^4 equation numerically. In the superluminal regime, the model possesses dnoidal and cnoidal waves. The former are modulationally unstable and…
We consider the dynamics of even solutions of the one-dimensional nonlinear Klein-Gordon equation $\partial_t^2 \phi - \partial_x^2 \phi + \phi - |\phi|^{2\alpha} \phi =0$ for $\alpha>1$, in the vicinity of the unstable soliton $Q$. Our…
Saddle-point configurations, such as the Euclidean bounce and sphalerons, are known to be difficult to find numerically. In this Letter we study a new method, Quartic Gradient Flow, to search for such configurations. The central idea is to…
We find that an oscillon can possess a characteristic double oscillation structure even though it results in a decay of a sphaleron which does not have any positive energy vibrational mode. We show that dynamics of such an oscillon can…
In this paper, we provide new exact solutions of nonlinear Klein-Gordon ($\phi^4$) equation in $1+1$-dimension. For simplicity, we focus on the static equation and ignore the time-dependence. The symmetric $\phi^4$ equation has played an…
We discuss spherically symmetric static solutions of the Einstein-Klein-Gordon equations for a real scalar field with a mass and a quartic self-interaction term. As for the massless case the solutions have a naked singularity at the origin.…
The cooling algorithm for saddle points presented in ref. [1] is generalized to obtain static classical solutions of the SU(2)-Higgs field theory in the limit of infinite Higgs self-coupling. The sphaleron energy obtained via this algorithm…
We study the stability of standing-waves solutions to a scalar non-linear Klein-Gordon equation in dimension one with a quadratic-cubic non-linearity. Orbits are obtained by applying the semigroup generated by the negative complex unit…
This paper is a detailed and self-contained study of the stability properties of periodic traveling wave solutions of the nonlinear Klein-Gordon equation $u_{tt}-u_{xx}+V'(u)=0$, where $u$ is a scalar-valued function of $x$ and $t$, and the…
The problem of linear instability of a nonlinear traveling wave in a canonical Hamiltonian system with translational symmetry subject to superharmonic perturbations is discussed. It is shown that exchange of stability occurs when energy is…
We consider effectively one-dimensional planar and radial kinks in two-dimensional nonlinear Klein-Gordon models and focus on the sine-Gordon model and the $\phi^4$ variants thereof. We adapt an adiabatic invariant formulation recently…
We consider a Hamiltonian systems which is invariant under a one-parameter unitary group. We give a criterion for the stability and instability of bound states for the degenerate case. We apply our theorem to the single power nonlinear…
It is proven that there are precisely $n$ odd-parity sphaleron-like unstable modes of the $n$-th Bartnik-McKinnon soliton and the $n$-th non-abelian black hole solution of the Einstein-Yang-Mills theory for the gauge group $SU(2)$.
Quadratic scale-invariant gravity non minimally coupled to a scalar field provides a competitive model for inflation, characterized by the transition from an unstable to a stable fixed point, both characterized by constant scalar field…
A model of nonlinear elastic medium with internal structure is considered. The medium is assumed to contain cavities, microcracks or blotches of substances that differ sharply in physical properties from the base material. To describe the…
We solve numerically the Einstein-Klein-Gordon system with spherical symmetry, for a massive real scalar field endowed with a quartic self-interaction potential, and obtain the so-called $\Phi^4$-oscillatons which is the short name for…
Starting from the equation of motion of the quantum operator of a real scalar field phi in de Sitter space-time, a simple differential equation is derived which describes the evolution of quantum fluctuations <phi^2> of this field. Full de…
Fourth-order semilinear parabolic equations of the Cahn--Hilliard-type (01) u_t + \D^2 u = \g u \pm \D (|u|^{p-1}u) in \Omega \times \re_+, are considered in a smooth bounded domain $\O \subset \ren$ with Navier-type boundary conditions on…