KP web-solitons from wave patterns: an inverse problem

Physics and Mathematics of Nonlinear Phenomena 2013

Chakravarty, Sarbarish^1 ; Kodama, Yuji^2

Department of Mathematics, University of Colorado, Colorado Springs, CO 80933, United States^1

Department of Mathematics, Ohio State University, Columbus, OH 43210, United States^2

关键词: Kadomtsev-Petviashvili equation;    Long wavelength;    Non-stationary dynamics;    Nonlinear interactions;    Propagating waves;    Shallow water waves;    Small amplitude;    Soliton solutions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/482/1/012007/pdf
DOI  :  10.1088/1742-6596/482/1/012007

来源: IOP

【 摘 要 】

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.