On modulational instabilities in discretisations of the Korteweg-de Vries equation

DOI10.1016/0021-9991(88)90009-5zbMath0657.76016OpenAlexW2010438667MaRDI QIDQ1111407

David M. Sloan

Publication date: 1988

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9991(88)90009-5

zbMATH Keywords

Korteweg-de Vries equationleap-frog discretisationsnonlinear instabilitiesside-band Fourier modes

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Partial differential equations of mathematical physics and other areas of application (35Q99) Applications to the sciences (65Z05)

Related Items (6)

Numerical methods for the solution of the third- and fifth-order dispersive Korteweg-de Vries equations ⋮ Global spectral analysis: review of numerical methods ⋮ Exact analysis of nonlinear instability in a discrete Burgers' equation ⋮ A discrete multiple scales analysis of a discrete version of the Korteweg-de Vries equation ⋮ A scheme with a higher-order discrete invariant for the KdV equation ⋮ Derivative instability of some schemes for the Korteweg-de Vries equation

Cites Work

• Focusing: A mechanism for instability of nonlinear finite difference equations
• On nonlinear instabilities in leap-frog finite difference schemes
• Studies in numerical nonlinear instability. II. A new look at \(u_ t+uu_ x=0\)
• An explicit finite-difference scheme with exact conservation properties
• The disintegration of wave trains on deep water Part 1. Theory
• On the Instability of Leap-Frog and Crank-Nicolson Approximations of a Nonlinear Partial Differential Equation

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