Single soliton solution to the extended KdV equation over uneven depth

Eur Phys J E Soft Matter. 2017 Nov 20;40(11):100. doi: 10.1140/epje/i2017-11591-7.

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.

Keywords: Flowing matter: Nonlinear Physics.