A small time solutions for the Korteweg–de Vries equation

摘要

In this paper a heat balance integral (HBI) method is applied to the one-dimensional non-linear Korteweg–de Vries (KdV) equation prescribed by appropriate homogenous boundary conditions and a set of initial conditions to obtain its approximate analytical solutions at small times. It is shown that the HBI solutions obtained by the method may be used effectively at small times when the exact solution of the KdV equation is not known.