Department of Civil Engineering, Technological & Educational Institute of Patras, 1 M. Alexandrou Street, Koukouli, 263 34 Patras, Greece
Copyright © 2010 V. Marinakis. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We show that a nonlinear equation that represents third-order
approximation of long wavelength, small amplitude waves of inviscid and incompressible
fluids is integrable for a particular choice of its parameters, since in this
case it is equivalent with an integrable equation which has recently appeared in
the literature. We also discuss the integrability of both second- and third-order
approximations of additional cases.