A direct and inverse problem for wave crests modelled by interactions of two solitons

@inproceedings{Peterson2006ADA,
title={A direct and inverse problem for wave crests modelled by interactions of two solitons},
author={P. Peterson},
year={2006}
}

The paper addresses a new “inverse” problem for reconstructing the amplitudes of 2D surface waves from observation of the wave patterns (formed by wave crests). These patterns will depend on the amplitudes because of nonlinear effects. We show that the inverse problem can be solved when the waves are modelled by an equation that supports soliton solutions. Specifically, the explicit solution to the inverse problem is derived for two interacting solitons of the KP (Kadomtsev-Petviashvili… CONTINUE READING