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Advances in Mathematical Physics
Volume 2010, Article ID 329586, 5 pages
Research Article

Higher-Order Equations of the KdV Type are Integrable

Department of Civil Engineering, Technological & Educational Institute of Patras, 1 M. Alexandrou Street, Koukouli, 263 34 Patras, Greece

Received 5 January 2010; Accepted 27 January 2010

Academic Editor: Jan Hesthaven

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.