A small time solutions for the Korteweg-de Vries equation

@article{Kutluay2000AST,
title={A small time solutions for the Korteweg-de Vries equation},
author={Selçuk Kutluay and A. Refik Bahadir and A. {\"O}zdes},
journal={Applied Mathematics and Computation},
year={2000},
volume={107},
pages={203-210}
}

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 eectively at small times when the exact solution of the KdV equation is not known. Ó 2000 Elsevier Science Inc. All rights reserved.