KP web-solitons from wave patterns: an inverse problem

Abstract

Nonlinear interactions among small amplitude, long wavelength, obliquely propagating waves on the surface of shallow water often generate web-like patterns. In this article, we discuss how line-soliton solutions of the Kadomtsev-Petviashvili (KP) equation can approximate such web-pattern in shallow water wave. We describe an "inverse problem" which maps a certain set of measurable data from the solitary waves in the given pattern to the parameters required to construct an exact KP soliton that describes the non-stationary dynamics of the pattern. We illustrate the inverse problem using explicit examples of shallow water wave pattern.