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.

1.
See the appendix for a derivation of the correction to the usual shallow‐water equations.
2.
C. S. Gardner and G. K. Morikawa, Courant Institute of Mathematical Sciences, New York University Report NYU‐9082, 1960 (unpublished).
3.
H.
Washimi
and
T.
Taniuti
,
Phys. Rev. Letters
17
,
996
(
1966
).
This content is only available via PDF.
You do not currently have access to this content.