KP solitons from tropical limits. (January 2023)

• Record Type: Journal Article
• Authors: Agostini, Daniele; Fevola, Claudia; Mandelshtam, Yelena; Sturmfels, Bernd
• Is Part Of: Journal of symbolic computation. Volume 114(2023)
• Page Start: 282
• Page End: 301
• Publication Date: 2023-01
• Subjects: KP equation -- Soliton solutions -- Theta function -- Delaunay polytope -- Sato Grassmannian -- Riemann-Roch space; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.04.009
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We study solutions to the Kadomtsev-Petviashvili equation whose underlying algebraic curves undergo tropical degenerations. Riemann's theta function becomes a finite exponential sum that is supported on a Delaunay polytope. We introduce the Hirota variety which parametrizes all tau functions arising from such a sum. We compute tau functions from points on the Sato Grassmannian that represent Riemann-Roch spaces and we present an algorithm that finds a soliton solution from a rational nodal curve.