Eur. Phys. J. E (2017) 40: 100
https://doi.org/10.1140/epje/i2017-11591-7

Regular Article

Single soliton solution to the extended KdV equation over uneven depth

¹ Department of Physics, University of Warwick, CV4 7A, Coventry, UK
² Institute of Physics, Faculty of Physics and Astronomy, University of Zielona Góra, Szafrana 4a, 65-246, Zielona Góra, Poland
³ National Centre for Nuclear Research, Hoża 69, 00-681, Warszawa, Poland
⁴ Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-246, Zielona Góra, Poland

^* e-mail: p.rozmej@if.uz.zgora.pl

Received: 4 August 2017
Accepted: 31 October 2017
Published online: 20 November 2017

Abstract

In this note we look at the influence of a shallow, uneven riverbed on a soliton. The idea consists in an approximate transformation of the equation governing wave motion over an uneven bottom to an equation for a flat one for which the exact solution exists. The calculation is one space dimensional, and so corresponds to long trenches or banks under wide rivers or oceans.