Laboratory realization of KP-solitons

Physics and Mathematics of Nonlinear Phenomena 2013

Yeh, Harry^1 ; Li, Wenwen^2

Oregon State University, Corvallis, OR 97331, United States^1

URS Corporation, Los Angeles, CA 90017, United States^2

关键词: Asymptotic behavior of the solutions;    Fluorescent methods;    Kadomtsev-Petviashvili equation;    Laboratory environment;    Optical measurement techniques;    Physical interpretation;    Temporal and spatial variation;    Water surface profile;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/482/1/012046/pdf
DOI  :  10.1088/1742-6596/482/1/012046

来源: IOP

【 摘 要 】

Kodama and his colleagues presented a classification theorem for exact soliton solutions of the quasi-two-dimensional Kadomtsev-Petviashvili (KP) equation. The classification theorem is related to non-negative Grassmann manifold, Gr(N, M) that is parameterized by a unique chord diagram based on the derangement of the permutation group. The cord diagram can infer the asymptotic behavior of the solution with arbitrary number of line solitons. Here we present the realization of a variety of the KP soliton formations in the laboratory environment. The experiments are performed in a water tank designed and constructed for precision experiments for long waves. The tank is equipped with a directional-wave maker, capable of generating arbitrary-shaped multi-dimensional waves. Temporal and spatial variations of water-surface profiles are captured using the Laser Induces Fluorescent method-a nonintrusive optical measurement technique with sub-millimeter precision. The experiments yield accurate anatomy of the KP soliton formations and their evolution behaviors. Physical interpretations are discussed for a variety of KP soliton formations predicted by the classification theorem.