Graduation Year

2005

Document Type

Thesis

Degree

M.A.

Degree Granting Department

Mathematics and Statistics

Major Professor

Dr.Wen - Xiu Ma.

Co-Major Professor

Dr.Youcheng You

Keywords

The kp equation, Solitons, Interaction patterns, Spider-web-like structures, Levels of intersection

Abstract

In this thesis, the interaction pattern for a class of soliton solutions of the Kadomtsev- Petviashvili (KP) equation is analyzed. The complete asymptotic properties of the soliton solutions for are determined. The resonance characteristic of two sub-classes of the soliton solutions, in which incoming line solitons for interact to form outgoing line solitons for , is described. These two specific sub-classes of -soliton solutions are the following: 1) [(2, 3), (2, 4), (2, 5)], 2) [(3, 2), (3, 3), (3, 4)]. The intermediate solitons and the interaction regions of the above soliton solutions are determined, and their various interaction patterns are explored. Maple and Mathematica are used to get the 3 dimensional plots and contour plots of the soliton solutions to show their interaction patterns. Finally, the spider-web-structures of the discussed solitons of the KP equation are displayed.

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