Using a density matrix description in space we study the evolution of wavepackets in a fluctuating space–time background. We assume that space–time fluctuations manifest as classical fluctuations of the metric. From the non–relativistic limit of a non-minimally coupled Klein–Gordon equation we derive a Schrödinger equation with an additive gaussian random potential. This is transformed into an ...

This paper is devoted to the study of solitary waves and solitons whose existence is related to the ratio energy/charge. These solitary waves are called hylomorphic. This class includes the Q-balls, which are spherically symmetric solutions of the nonlinear Klein-Gordon equation (NKG), as well as solitary waves and vortices which occur, by the same mechanism, in the nonlinear Schroedinger equat...

We consider Galerkin finite element methods for the nonlinear Klein-Gordon equation, giving the first optimal-order energy norm semidiscrete error estimates for non-Lipschitz nonlinearity. The result holds quite generally in one and two space dimensions and under a certain growth restriction in three. We also discuss some time stepping strategies and present numerical results.

where u = u(t, x) ∈ C(R,R) and V (x) ∈ C(R,R), by using the method of separation of variables (SV). Equations belonging to class (1) are widely used in the modern quantum physics and can be related to other linear and nonlinear equations of mathematical physics (these relations will be discussed below, at the end of the article). In particular, class (1) contains the d’Alembert equation (with V...

We construct infinitely many real-valued, time-periodic breather solutions of power-type nonlinear wave equations. These are obtained from critical points a dual functional and they weakly localized in space. Our abstract framework allows to find similar existence results for the Klein-Gordon equation or biharmonic

In this paper the dynamics of the interaction of attosecond laser pulses with matter is investigated. It will be shown that the master equation: modified Klein-Gordon equation describes the propagation of the heatons. Heatons are the thermal wave packets. When the duration of the laser pulses ∆t is of the order of attosecond the heatonthermal wave packets are nondispersive objects. For ∆t → ∞ t...

In the present paper, we work out the eigenfunctions of spinless particles bound in a one-dimensional linear finite range, attractive potential well, treating it as a time-like component of a four-vector. We show that the one-dimensional stationary Klein-Gordon equation is reduced to a standard differential equation, whose solutions, consistent with the boundary conditions, are the parabolic cy...

The effects, upon the Klein–Gordon field, of nonconformal stochastic metric fluctuations, are analyzed. It will be shown that these fluctuations allow us to consider an effective mass, i.e., the mass detected in a laboratory is not the parameter appearing in the Klein–Gordon equation, but a function of this parameter and of the fluctuations of the metric. In other words, in analogy to the case ...