Korteweg-de Vries Equation and Generalizations. III. Derivation of the Korteweg-de Vries Equation and Burgers Equation

1 March 1969

journal article
Published by AIP Publishing in Journal of Mathematical Physics

Vol. 10 (3) , 536-539
https://doi.org/10.1063/1.1664873

Abstract

The Korteweg-de Vries equation and the Burgers equation are derived for a wide class of nonlinear Galilean-invariant systems under the weak-nonlinearity and long-wavelength approximations. The former equation is shown to be a limiting form for nonlinear dispersive systems while the latter is a limiting form for nonlinear dissipative systems.

Keywords

BURGERS EQUATION
DISSIPATIVE SYSTEM
MAGNETOHYDRODYNAMICS
KORTEWEG DE VRIES EQUATION
DIFFERENTIAL EQUATION

This publication has 1 reference indexed in Scilit:

Propagation of Ion-Acoustic Solitary Waves of Small Amplitude
Physical Review Letters, 1966