2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160171This 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.18 pages, 4 figures. Added some minor comments. To appear in AMS Contemporary MathematicsExactly Solvable and Integrable SystemsMathematical PhysicsCombinatoricstext