Korteweg-de Vries Equation

Author

Eric W. Weisstein
June 2, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/DifferentialEquations/Korteweg-deVriesEquation.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Korteweg-deVriesEquation.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Non-Dimensional

DSolve[D[u[t,x],t]+D[u[t,x],{x,3}]-6u[t,x]D[u[t,x],x]==0,u[t,x],{t,x}]

Dimensional Equation

((∂η)/(∂t))=(3/2)(Sqrt[(g/h)])(η ((∂η)/(∂x))+(2/3)((∂η)/(∂x))+(1/3)σ(((∂^3)η)/(∂(x^3))))