In this thesis, the interaction pattern for a class of soliton solutions of the Kadomtsev- Petviashvili (KP) equation (−4ut + uxxx + 6uux )x + 3uyy = 0 is analyzed. The complete asymptotic properties of the soliton solutions for y → ±∞ are determined. The resonance characteristic of two sub-classes of the soliton solutions, in which N- incoming line solitons for y → −∞ interact to form N+ outgoing line solitons for y → ∞, is described. These two specific sub-classes of (N-,N+)-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.
| Identifer | oai:union.ndltd.org:USF/oai:scholarcommons.usf.edu:etd-1885 |
| Date | 08 July 2005 |
| Creators | Tippabhotla, Anupama |
| Publisher | Scholar Commons |
| Source Sets | University of South Flordia |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Graduate Theses and Dissertations |
| Rights | default |
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