Related papers: Local linearization for the nonlinear damped stoch…
We study the bi-parameter local linearization of the one-dimensional nonlinear stochastic wave equation driven by a Gaussian noise, which is white in time and has a spatially homogeneous covariance structure of Riesz-kernel type. We…
For the $1+1$ dimensional damped stochastic Klein-Gordon equation, we show that random singularities associated with the law of the iterated logarithm exist and propogate in the same way as the stochastic wave equation. This provides…
We consider difference schemes for nonlinear time fractional Klein-Gordon type equations in this paper. A linearized scheme is proposed to solve the problem. As a result, iterative method need not be employed. One of the main difficulties…
We consider a discrete nonlinear Klein-Gordon equations with damping and external drive. Using a small amplitude ansatz, one usually approximates the equation using a damped, driven discrete nonlinear Schr\"odinger equation. Here, we show…
The numerical approximation of the semilinear Klein--Gordon equation in the $d$-dimensional space, with $d=1,2,3$, is studied by analyzing the consistency errors in approximating the solution. By discovering and utilizing a new cancellation…
We study the 1D Klein-Gordon equation with variable coefficient nonlinearity. This problem exhibits an interesting resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…
We investigate thermalization and symmetry-breaking in a nonlinear stochastic Klein-Gordon equation on a spatial lattice, taking into account damping, nonlinear interaction, and stochastic forcing terms reduced by a perturbative solution…
We present a new complex non-stationary particle-like solution of the non-linear Klein-Gordon equation with several spatial variables. The construction is based on reduction to an ordinary differential equation.
We study the non relativistic and ultra relativistic limits in the two-dimensional nonlinear damped Klein-Gordon equation driven by a space-time white noise on the torus. In order to take the limits, it is crucial to clarify the parameter…
We study the 1D Klein-Gordon equation with variable coefficient cubic nonlinearity. This problem exhibits a striking resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…
Theories of gravity in which the metric is fundamentally classical predict stochastic fluctuations in the gravitational field. In this article, we study the stochastic Klein-Gordon equation as a starting point to understand the…
We consider the asymptotic behavior of small global-in-time solutions to a 1D Klein-Gordon equation with a spatially localized, variable coefficient quadratic nonlinearity and a non-generic linear potential. The purpose of this work is to…
We show that the Schr\"{o}dinger-Newton equation, which describes the nonlinear time evolution of self-gravitating quantum matter, can be made compatible with the no-signaling requirement by elevating it to a stochastic differential…
In this article, we consider the stochastic Cahn--Hilliard equation driven by multiplicative space-time white noise with diffusion coefficient of sublinear growth. By introducing the spectral Galerkin method, we first obtain the…
In this article, we derive the scalar parametrized Klein-Gordon equation from the formal information theory framework. The least biased probability distribution is obtained, and the scalar equation is recast in terms of a Fokker-Planck…
In this paper, we consider a semi-linear stochastic strongly damped wave equation driven by additive Gaussian noise. Following a semigroup framework, we establish existence, uniqueness and space-time regularity of a mild solution to such…
In this note, we establish a bi-parameter linear localization of the one-dimensional stochastic wave equation with a multiplicative space-time white noise forcing.
We consider a nonlinear Klein--Gordon equation in the nonrelativistic limit regime with highly oscillatory initial data in the form of a modulated plane wave. In this regime, the solution exhibits rapid oscillations in both time and space,…
In this paper, we study large time behavior of complex-valued solutions to nonlinear Klein-Gordon equation with a gauge invariant quadratic nonlinearity in two spatial dimensions. To find a possible asymptotic behavior, we consider the…
For a damped wave (or Klein-Gordon) equation on a bounded domain, with a focusing power-like nonlinearity satisfying some growth conditions, we prove that a global solution is bounded in the energy space, uniformly in time. Our result…