Related papers: A General Theory of Oscillon Dynamics
We consider long time evolution of small solutions to general multispeed Klein-Gordon systems in 3+1 dimensions. We prove that such solutions are always global and scatter to a linear flow, thus extending previous partial results. The main…
We study cosmological models using dynamical systems and averaging methods, encompassing flat and open FLRW geometries as well as the LRS Bianchi types I, III, and V. Under mild regularity and frequency-scaling assumptions, we obtain a…
The Stuart-Landau oscillator generalized to $D > 2$ dimensions has SO($D$) rotational symmetry. We study the collective dynamics of a system of $K$ such oscillators of dimensions $D =$ 3 and 4, with coupling chosen to either preserve or…
In this paper, we discuss the dynamics of two- scalar-field cosmological models. Unlike in the situation of exponential potential, we find that there are late-time attractors in which one scalar field dominates the energy density of…
We study I-balls/oscillons, which are long-lived, quasi-periodic, and spatially localized solutions in real scalar field theories. Contrary to the case of Q-balls, there is no evident conserved charge that stabilizes the localized…
It was previously shown by one of us that in any static, non-globally-hyperbolic, spacetime it is always possible to define a sensible dynamics for a Klein-Gordon scalar field. The prescription proposed for doing so involved viewing the…
In recent researches of the dynamics of solitons, it is gradually revealed that oscillation modes play a crucial role when we analyze the dynamics of solitons. Some dynamical properties of solitons on external potentials are studied with…
We study the solutions to the Klein-Gordon equation for the massive scalar field in the universal covering space of two-dimensional anti-de Sitter space. For certain values of the mass parameter, we impose a suitable set of boundary…
The attractors of a dynamical system govern its typical long-term behaviour. The presence of many attractors is significant as it means the behaviour is heavily dependent on the initial conditions. To understand how large numbers of…
Gravitational stability of torsion and inflaton field in a four-dimensional spacetime de Sitter solution in scalar-tensor cosmology where Cartan torsion propagates is investigated in detail. Inflaton and torsion evolution equations are…
If the inflaton is a heavy scalar field, it may equilibrate slower than some other degrees of freedom, e.g. non-Abelian gauge bosons. In this case, perturbations in the inflaton field and in a thermal plasma coexist from a given moment…
In this paper, we study the cosmological dynamics of scalar fields with O(N) symmetry in general potentials. We compare the phase space of the dynamical systems of the quintessence and phantom and give the conditions for the existence of…
Turbulent flows present rich dynamics originating from non-trivial energy fluxes across scales, non-stationary forcings and geometrical constraints. This complexity manifests in non-hyperbolic chaos, randomness, state-dependent persistence…
We establish the global existence and scattering for small and localized solutions of the Klein-Gordon-Schr\"{o}dinger system in three dimensions. The system consists of coupled semilinear Schr\"{o}dinger and Klein-Gordon equations with…
Recently a Hamiltonian formulation for the evolution of the universe dominated by multiple oscillatory scalar fields was developed by the present author and was applied to the investigation of the evolution of cosmological perturbations on…
We present results from a detailed study of spherically symmetric Einstein-massless-scalar field dynamics with a negative cosmological constant in four to nine spacetime dimensions. This study is the first to present a detailed examination…
We consider a $D$-dimensional cosmological model with a dilaton field and two $(D-d-1)$-form field strengths which have nonvanishing fluxes in extra dimensions. Exact solutions for the model with a certain set of couplings are obtained by…
Many real world systems exhibit cyclic behavior that is, for example, due to the nearly harmonic oscillations being perturbed by the strong fluctuations present in the regime of significant non-linearities. For the investigation of such…
In this manuscript using the asymptotic method of multiscale nonlinear theory we construct a nonlinear theory of the appearance of large-scale structures in the stratified conductive medium with the presence of small-scale oscillations of…
We develop a trajectory construction of solutions to the massless wave equation in n+1 dimensions and hence show that the quantum state of a massive relativistic system in 3+1 dimensions may be represented by a stand-alone four-dimensional…