Numerical simulation of the stochastic Korteweg-de Vries equation

DOI10.1016/S0167-2789(99)00072-XzbMath0948.76038MaRDI QIDQ1808362

Arnaud Debussche, Jacques Printems

Publication date: 6 December 1999

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

finite elementsleast-squaresKorteweg-de Vries equationnoise amplitudeevolution of solitonshomogeneous noise

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Solitary waves for incompressible inviscid fluids (76B25) Stochastic analysis applied to problems in fluid mechanics (76M35) Finite element methods applied to problems in fluid mechanics (76M10) Stochastic particle methods (65C35)

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Cites Work

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• Analytical and numerical aspects of certain nonlinear evolution equations. III. Numerical, Korteweg-de Vries equation
• Transient waves produced by flow past a bump
• Approximations of the KdV equation by least squares finite elements
• On the stochastic Korteweg-de Vries equation
• The stochastic Korteweg-de Vries equation in \(L^2(\mathbb{R})\)
• Implicit scheme for stochastic parabolic partial differential equations driven by space-time white noise
• Effect of Random Inhomogeneities on Nonlinear Propagation of Water Waves
• On the excitation of long nonlinear water waves by a moving pressure distribution
• The stochastic, damped KdV equation
• Resonant Flow of a Rotating Fluid Past an Obstacle: The General Case
• Conerservative and Nonconservative Schemes for the Solution of the Nonlinear Schrödinger Equation
• Weak Approximation of Solutions of Systems of Stochastic Differential Equations
• Generation of upstream advancing solitons by moving disturbances
• Water waves in shallow channels of rapidly varying depth
• Resonant Generation of Finite-Amplitude Waves by Flow Past Topography on a β -Plane
• Approximate Integration of Stochastic Differential Equations
• Conservative, high-order numerical schemes for the generalized Korteweg—de Vries equation
• The initial-value problem for the forced Korteweg-de Vries equation