The Stochastic Korteweg–de Vries Equation inL2(R)
نویسندگان
چکیده
منابع مشابه
Numerical studies of the stochastic Korteweg-de Vries equation
We present numerical solutions of the stochastic Korteweg-de Vries equation for three cases corresponding to additive time-dependent noise, multiplicative space-dependent noise and a combination of the two. We employ polynomial chaos for discretization in random space, and discontinuous Galerkin and finite difference for discretization in physical space. The accuracy of the stochastic solutions...
متن کاملRare-Event Simulation for the Stochastic Korteweg--de Vries Equation
An asymptotic analysis of the tail probabilities for the dynamics of a soliton wave U(x, t) under a stochastic time-dependent force is developed. The dynamics of the soliton wave U(x, t) is described by the Korteweg–de Vries (KdV) equation with homogeneous Dirichlet boundary conditions under a stochastic time-dependent force, which is modeled as a time-dependent Gaussian noise with amplitude . ...
متن کاملNumerical simulation of the stochastic Korteweg–de Vries equation
In this work, we numerically investigate the influence of a homogeneous noise on the evolution of solitons for the Korteweg–de Vries equation. Our numerical method is based on finite elements and least-squares. We present numerical experiments for different values of noise amplitude and describe different types of behaviours. ©1999 Elsevier Science B.V. All rights reserved.
متن کاملRare-event Simulation for Stochastic Korteweg-de Vries Equation
An asymptotic analysis of the tail probabilities for the dynamics of a soliton wave U(x, t) under a stochastic time-dependent force is developed. The dynamics of the soliton wave U(x, t) is described by the Korteweg-de Vries Equation with homogeneous Dirichlet boundary conditions under a stochastic time-dependent force, which is modeled as a time-dependent Gaussian noise with amplitude . The ta...
متن کاملConvergence of a semi-discrete scheme for the stochastic Korteweg–de Vries equation
In this article, we prove the convergence of a semi-discrete scheme applied to the stochastic Korteweg–de Vries equation driven by an additive and localized noise. It is the Crank–Nicholson scheme for the deterministic part and is implicit. This scheme was used in previous numerical experiments on the influence of a noise on soliton propagation [8, 9]. Its main advantage is that it is conservat...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1999
ISSN: 0022-0396
DOI: 10.1006/jdeq.1998.3548