Oblique Soliton-Soliton Interactions in the Laboratory Tank
Friday, October 17, 2014 - 9:00am - 9:50am
Exact soliton solutions of the quasi-two-dimensional Kadomtsev-Petviashvili (KP) equation and its classification theorem (by Kodama) are available. The classification theorem is related to non-negative Grassmann manifold 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. Temporal and spatial variations of water-surface profiles are captured using the Laser Induces Fluorescent method. 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. This problem is relevant to tsunami-tsunami interactions on a continental shelf.