On the dispersionless Davey-Stewartson hierarchy: the tau function, the Riemann-Hilbert problem and the Hamilton-Jacobi theory

TL;DR

This paper investigates the dispersionless Davey-Stewartson hierarchy, focusing on its tau function, Riemann-Hilbert problem, and Hamilton-Jacobi theory, revealing its integrable structure and symmetries.

Contribution

It introduces the construction of the dDS hierarchy via eigenfunctions and explores its associated tau function, Riemann-Hilbert problem, and Hamilton-Jacobi framework.

Findings

Construction of the dDS hierarchy using eigenfunctions

Analysis of the tau function related to dDS

Formulation of the Riemann-Hilbert problem and Hamilton-Jacobi theory for dDS

Abstract

The dDS (dispersionless Davey-Stewartson) hierarchy is constructed by two eigenfunctions of a special vector field. This hierarchy consists the infinite symmetries of the dDS system. Further, this paper explores the tau function, the Riemann-Hilbert problem and Hamilton-Jacobi theory related to dDS hierarchy.