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

Abstract

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.

arXiv comment18 pages, 4 figures. Added some minor comments. To appear in AMS Contemporary Mathematics

References in corpus (4)

• Total positivity, Grassmannians, and networks
• On a family of solutions of the KP equation which also satisfy the Toda lattice hierarchy
• Young diagrams and N-soliton solutions of the KP equation
• Degenerate Four Virtual Soliton Resonance for KP-II

Cited by in corpus (6)

• KP solitons and total positivity for the Grassmannian
• Soliton solutions of the KP equation and application to shallow water waves
• The Deodhar decomposition of the Grassmannian and the regularity of KP solitons
• Kadomtsev-Petviashvili II equation: Structure of asymptotic soliton webs
• Soliton Interaction In the Modified Kadomtsev-Petviashvili-(II) Equation
• The resonant structure of Kink-Solitons in the Modified KP Equation