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

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