Related papers: A General Theory of Oscillon Dynamics
Recent perturbative studies have shown the existence of long-lived, quasi-stationary configurations of scalar fields around black holes. In particular, such configurations have been found to survive for cosmological timescales, which is a…
We investigate the nonequilibrium evolution of a scalar field in (2+1) dimensions. The field is set in a double-well potential in contact (open) or not (closed) with a heat bath. For closed systems, we observe the synchronized emergence of…
On a bounded three-dimensional smooth domain, we consider the generalized oscillon equation with Dirichlet boundary conditions, with time-dependent damping and time-dependent squared speed of propagation. Under structural assumptions on the…
The effect of rapid oscillations, related to large dispersion terms, on the dynamics of dissipative evolution equations is studied for the model examples of the 1D complex Ginzburg-Landau and the Kuramoto-Sivashinsky equations. Three…
Spherically symmetric oscillatons (also referred to as oscillating soliton stars) i.e. gravitationally bound oscillating scalar lumps are considered in theories containing a massive self-interacting real scalar field coupled to Einstein's…
We investigate the dynamics of a three-dimensional system modeling a molecular mechanism for the circadian rhythm in Drosophila. We first prove the existence of a compact attractor in the region with biological meaning. Under the assumption…
We study the collision dynamics of localized oscillons in two classes of $(1+1)$-dimensional scalar field theories with metastable false vacua, a normal class with a positive quartic self-interaction term and an inverted class with a…
We study oscillon/I-ball solutions in a real scalar version of the Friedberg-Lee-Sirlin (FLS) model. Using the two-timing analysis, we derive the conditions for oscillon solutions and explore multi-field oscillon configurations. In these…
Synchronisation and stability under periodic oscillatory driving are well-understood, but little is known about the effects of aperiodic driving, despite its abundance in nature. Here, we consider oscillators subject to driving with slowly…
We investigate the existence and behavior of oscillons in theories in which higher derivative terms are present in the Lagrangian, such as galileons. Such theories have emerged in a broad range of settings, from higher-dimensional models,…
In this study, we analyze solutions of the wave equation for scalar particles in a space-time with nontrivial topology. Solutions for the Klein--Gordon oscillator are found considering two configurations of this space-time. In the first…
In this article we consider a system of two Klein-Gordon equations, set on the $d$-dimensional box of size $L$, coupled through quadratic semilinear terms of strength $\varepsilon$ and evolving from well-prepared random initial data. We…
In this paper, we study the (1+3) dimensional massive Maxwell-Dirac system in the context of global existence and asymptotic behavior of solutions under the Lorenz gauge condition, as well as the modified and linear scattering phenomena for…
We study the classical dynamics of the Abelian Higgs model employing an asymptotic multiscale expansion method, which uses the ratio of the Higgs to the gauge field amplitudes as a small parameter. We derive an effective nonlinear…
Oscillons in a simple, 1-dimensional scalar field theory with a cubic potential are discussed. The theory has a classical sphaleron, whose decay generates a version of the oscillon. A good approximation to the small-amplitude oscillon is…
We investigate theoretically and numerically the dynamics of long-living oscillating coherent structures - bi-solitons - in the exact and approximate models for waves on the free surface of deep water. We generate numerically the…
The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are…
The global attraction is established for all finite energy solutions to a model $\mathbf{U}(1)$-invariant nonlinear Klein-Gordon equation in one dimension coupled to a finite number of nonlinear oscillators: We prove that {\it each finite…
Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional sub-dynamics.…
If a real scalar field is dominated by non-relativistic modes, then it approximately conserves its particle number and obeys an equation that governs a complex scalar field theory with a conserved global U(1) symmetry. From this fact, it is…