Journal of Ocean Engineering and Science

Volume 2, Issue 1

(1)A new integrable nonlocal modified KdV equation: Abundant solutions with distinct physical structures

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

Received 11 October 2016; accepted 7 November 2016
Available online 23 November 2016

Abstract
In this work we study a new integrable nonlocal modified Korteweg–de Vries equation (mKdV) which arises from a reduction of the AKNS scattering problem. We use a variety of distinct techniques to determine abundant solutions with distinct physical structures. We show that this nonlocal equation possesses a family of traveling solitary wave solutions that include solitons, kinks, periodic and singular solutions.
© 2017 Published by Elsevier B.V. on behalf of Shanghai Jiaotong University.
This is an open access article under the CC BY-NC-ND license. ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Keywords: Nonlocal modified KdV equation; Soliton solutions; Periodic solutions; Exponential solutions.