Remarks on combinatorial aspects of the KP equation

Abstract

Abstract. We survey several results connecting combinatorics and Wronskian solutions of the KP equation, contextualizing the successes of a recent approach introduced by Kodama, et. al. We include the necessary combinatorial and analytical background to present a formula for generalized KP solitons, compute several explicit examples, and indicate how such a perspective could be used to extend previous research relating line-soliton solutions of the KP equation with Grassmannians.

Integrable hierarchies, Hurwitz numbers and a branch point field in critical topologically massive gravity

“…In the last decades, several connections between combinatorics and the theory of integrable systems were discovered [44][45][46]. In particular, owing to recurrence relations governing the higher symmetries and conservation laws of integrable hierarchies, it is known that equations of integrable systems exhibit certain combinatorial structures.…”