Interaction Patterns and Web-Structures of Resonant Solitons of the Kadomtsev-Petviashvili Equation

Author

Anupama Tippabhotla, University of South Florida

Graduation Year

2005

Document Type

Thesis

Degree

M.A.

Degree Granting Department

Mathematics and Statistics

Major Professor

Wen-Xiu Ma, Ph.D.

Committee Member

Yuncheng You, Ph.D.

Committee Member

Athanassios G. Kartsatos, Ph.D.

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 (−4u_t + u_xxx + 6uu_x )_x + 3u_yy = 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). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/886