A generating function for the N-soliton solutions of the Kadomtsev-Petviashvili II equation

Details A generating function for the N-soliton solutions of the Kadomtsev-Petviashvili II equation A generating function for the N-soliton solutions of the Kadomtsev-Petviashvili II equation

2008-02-04

arxiv.org/abs/0802.0524v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

18 pages, 4 figures. Added some minor comments. To appear in AMS Contemporary Mathematics

Scientific paper

This work describes a classification of the $N$-soliton solutions of the Kadomtsev-Petviashvili II equation in terms of chord diagrams of N chords joining pairs of 2N points. The different classes of N-solitons are enumerated by the distribution of crossings of the chords. The generating function of the chord diagrams is expressed as a continued fraction, special cases of which are moment generating functions for certain kinds of $q$-orthogonal polynomials.

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