Journal of Ocean Engineering and Science

Volume 1, Issue 3

(1)The simplified Hirota’s method for studying three extended higher-order KdV-type equations

Abdul-Majid Wazwaz
Department of Mathematics, Saint Xavier University, Chicago, IL 60655, USA

Received 30 April 2016; accepted 28 June 2016
Available online 9 July 2016

Abstract
In this work we study three extended higher-order KdV-type equations. The Lax-type equation, the Sawada–Kotera-type equation and the CDG-type equation are derived from the extended KdV equation. We use the simplified Hirota’s direct method to derive multiple soliton solutions for each equation. We show that each model gives multiple soliton solutions, where the structures of the obtained solutions differ from the solutions of the canonical form of these equations.
© 2016 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ).

Keywords: Fifth-order KdV equation; Hirota’s method; Dispersion relation.