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arXiv · 0710.1456

Classification of the line-soliton solutions of KPII

Sarbarish Chakravarty·Yuji Kodama
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Abstract

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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Sarbarish Chakravarty, Yuji Kodama. 2007-10-08. Classification of the line-soliton solutions of KPII. https://doi.org/10.1088/1751-8113/41/27/275209

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