Classification of the line-soliton solutions of KPII

Details Classification of the line-soliton solutions of KPII Classification of the line-soliton solutions of KPII

2007-10-08

arxiv.org/abs/0710.1456v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

30 pages

Scientific paper

10.1088/1751-8113/41/27/275209

In the previous papers (notably, Y. Kodama, J. Phys. A 37, 11169-11190 (2004), and G. Biondini and S. Chakravarty, J. Math. Phys. 47 033514 (2006)), we found a large variety of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation. The line-soliton solutions are solitary waves which decay exponentially in $(x,y)$-plane except along certain rays. In this paper, we show that those solutions are classified by asymptotic information of the solution as $|y| \to \infty$. Our study then unravels some interesting relations between the line-soliton classification scheme and classical results in the theory of permutations.

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