Degree Granting Department
Mathematics and Statistics
Wen-Xiu Ma, Ph.D.
Yuncheng You, Ph.D.
Athanassios G. Kartsatos, Ph.D.
The KP equation, Solitons, Interaction Patterns, Spider-web-like structures, levels of Intersection
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.
Scholar Commons Citation
Tippabhotla, Anupama, "Interaction Patterns and Web-Structures of Resonant Solitons of the Kadomtsev-Petviashvili Equation" (2005). Graduate Theses and Dissertations.