Bethe Ansatz and Quantum Davey-Stewartson 1 System with Multicomponent in Two Dimensions

TL;DR

This paper derives exact solutions for a two-dimensional multicomponent quantum Davey-Stewartson 1 system by reducing it to one-dimensional problems and applying Bethe ansatz techniques.

Contribution

It introduces a novel approach to solving the multicomponent quantum DS1 system using Bethe ansatz and symmetry operators, providing exact solutions.

Findings

Exact solutions for the 2D multicomponent DS1 system

Reduction to two 1D delta-interaction problems

Application of symmetric and antisymmetric Young operators

Abstract

The quantum 2-component DS1 system was reduced to two 1D many-body problems with $\delta-$function interactions, which were solved by Bethe ansatz. Using the ansatz in ref.[1] and introducing symmetric and antisymmetric Young operators of the permutation group, we obtain the exact solutions for the system.