On the dispersionless Davey-Stewartson system: Hamiltonian vector fields Lax pair and relevant nonlinear Riemann-Hilbert problem for dDS-II system

TL;DR

This paper investigates the dispersionless limit of Davey-Stewartson systems, revealing their Hamiltonian structure, Lax pairs, and formulating nonlinear Riemann-Hilbert problems to facilitate inverse scattering analysis.

Contribution

It introduces a Hamiltonian vector field Lax pair and constructs nonlinear Riemann-Hilbert problems for the dispersionless Davey-Stewartson II system, advancing integrable systems analysis.

Findings

Derived the Hamiltonian vector field Lax pair for dDS-II

Constructed nonlinear Riemann-Hilbert problems with symmetries for dDS-II

Facilitated the application of inverse scattering transform to dDS-II

Abstract

In this paper, the semiclassical limit of Davey-Stewartson systems are studied. It shows that these dispersionless limited integrable systems of hydrodynamic type, which are defined as dDS (dispersionless Davey-Stewartson) systems, are arisen from the commutation condition of Lax pairs of one-parameter vector fields. The relevant nonlinear Riemann-Hilbert problems with some symmetries for the dDS-II system are also constructed. This kind of Riemann-Hilbert problems are meaningful for applying the formal inverse scattering transform method, recently developed by Manakov and Santini, to study the dDS-II system .