The N-soliton solution of extended Korteweg-de Vries equation and SAR image simulation of internal solitary wave propagation

¹ State Key Laboratory of Software Development Environment, School of Computer Science and Engineering, Beihang University, Beijing 100191, P.R. China
² LMIB and School of Mathematics and System Sciences, Beihang University, Beijing 100191, P.R. China

^a e-mail: zhangyp@nlsde.buaa.edu.cn

Received: 30 July 2013
Revised: 8 October 2013
Accepted: 27 January 2014
Published online: 26 September 2014

Abstract

The extended Korteweg-de Vries (eKdV) equation is an important model for the description of internal solitary waves (ISWs) in shallow seas. The N-soliton solution of the eKdV equation is investigated by Hirota bilinear method. Direct simulation of the eKdV equation is performed for several ISWs phenomena including polarity conversion, packets and collisions by virtue of the N-soliton solution. Synthetic aperture radar (SAR) image simulations of those phenomena are also presented. Furthermore, the comparison between the simulated SAR image and the observed SAR image in the South China sea is provided, which shows that the N-soliton solution may describe various ISWs phenomena.