A universal form for the emergence of the Korteweg–de Vries equation

DOI10.1098/rspa.2012.0707zbMath1371.35244OpenAlexW2129544565MaRDI QIDQ5362140

Thomas J. Bridges

Publication date: 29 September 2017

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.2012.0707

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15)

Related Items (13)

Dimension breaking from spatially-periodic patterns to KdV planforms ⋮ Reduction to modified KdV and its KP-like generalization via phase modulation ⋮ On the Elliptic-Hyperbolic Transition in Whitham Modulation Theory ⋮ Phase dynamics of periodic wavetrains leading to the 5th order KP equation ⋮ Phase dynamics of the Dysthe equation and the bifurcation of plane waves ⋮ Double Degeneracy in Multiphase Modulation and the Emergence of the Boussinesq Equation ⋮ Nonlinear and nonlocal eigenvalue problems: variational existence, decay properties, approximation, and universal scaling limits ⋮ Whitham modulation equations, coalescing characteristics, and dispersive Boussinesq dynamics ⋮ On certain properties of the compact Zakharov equation ⋮ Nonlinear theory for coalescing characteristics in multiphase Whitham modulation theory ⋮ The modulation of multiple phases leading to the modified Korteweg–de Vries equation ⋮ Breakdown of the Whitham Modulation Theory and the Emergence of Dispersion ⋮ Dispersive dynamics in the characteristic moving frame

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