Related papers: White noise for KdV and mKdV on the circle
This paper advances the stochastic regularity theory for the Navier-Stokes equations by introducing a variable-intensity noise model within the Sobolev and Besov spaces. Traditional models usually assume constant-intensity noise, but many…
We use a white noise approach to study the problem of optimal inside control of a stochastic delay equation driven by a Brownian motion B and a Poisson random measure N. In particular, we use Hida-Malliavin calculus and the Donsker delta…
We study the mechanism of stochastic resonance in a two dimensional Landau Ginzburg equation perturbed by a white noise. We shortly review how to renormalize the equation in order to avoid ultraviolet divergences. Next we show that the…
The $b$-family-Kadomtsev-Petviashvili equation ($b$-KP) is a two dimensional generalization of the $b$-family equation. In this paper, we study the spectral stability of the one-dimensional small-amplitude periodic traveling waves with…
We develop an asymptotic limit theory for nonparametric estimation of the noise covariance kernel in linear parabolic stochastic partial differential equations (SPDEs) with additive colored noise, using space-time infill asymptotics. The…
In this paper we consider the two-dimensional stochastic Gross-Pitaevskii equation, which is a model to describe Bose-Einstein condensation at positive temperature. The equation is a complex Ginzburg-Landau equation with a harmonic…
Lie symmetry method is applied to investigate symmetries of the combined KdV-nKdV equation, that is a new integrable equation by combining the KdV equation and negative order KdV equation. Symmetries which are obtained in this article, are…
The paper is concerned with spatial and time regularity of solutions to linear stochastic evolution equation perturbed by L\'evy white noise "obtained by subordination of a Gaussian white noise". Sufficient conditions for spatial continuity…
We establish the existence of weak solutions to a class of distribution-dependent stochastic differential equations (DDSDEs) with possibly degenerate multiplicative noise and singular coefficients. Extending the weak existence techniques…
A functional integral technique is used to study the ultraviolet or short distance properties of the Kardar-Parisi-Zhang (KPZ) equation with white Gaussian noise. We apply this technique to calculate the one-loop effective potential for the…
By using Zvonkin's transformation and a two-step fixed point argument in distributions, the well-posedness and regularity estimates are derived for singular McKean-Vlasov SDEs with distribution dependent noise, where the drift contains a…
In this paper, we consider a system of $k$ second order non-linear stochastic partial differential equations with spatial dimension $d \geq 1$, driven by a $q$-dimensional Gaussian noise, which is white in time and with some spatially…
Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical…
The aim of this paper is the accurate numerical study of the KP equation. In particular we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end we first study…
We present a canonical phase space approach to stochastic systems described by Langevin equations driven by white noise. Mapping the associated Fokker-Planck equation to a Hamilton-Jacobi equation in the nonperturbative weak noise limit we…
In this paper we investigate the numerical solution of stochastic partial differential equations (SPDEs) for a wider class of stochastic equations. We focus on non-diagonal colored noise instead of the usual space-time white noise. By…
In this paper, we discuss a general approach to find periodic solutions bifurcating from equilibrium points of classical Vlasov systems. The main access to the problem is chosen through the Hamiltonian representation of any Vlasov system,…
This paper describes a novel numerical approach to find the statistics of the non-stationary response of scalar non-linear systems excited by L\'evy white noises. The proposed numerical procedure relies on the introduction of an integral…
We study the stability and dynamics of solitons in the Korteweg-de Vries (KdV) equation in the presence of noise and deterministic forcing. The noise is space-dependent and statistically translation-invariant. We show that, for small…
Periodic waves are investigated in a system composed of a Kuramoto-Sivashinsky - Korteweg-de Vries (KS-KdV) equation, which is linearly coupled to an extra linear dissipative equation. The model describes, e.g., a two-layer liquid film…