# Exact solutions by integrals of the non-stationary elliptic Calogero-Sutherland equation

## TL;DR

This paper develops explicit integral solutions for the non-stationary elliptic Calogero-Sutherland equation, offering new integral representations of elliptic Jack polynomials, advancing understanding of elliptic integrable systems.

## Contribution

It introduces a method using generalized kernel functions to construct explicit integral solutions for the elliptic Calogero-Sutherland model, including elliptic Jack polynomials.

## Key findings

- Explicit integral representations of solutions are derived.
- New integral forms of elliptic Jack polynomials are provided.
- The approach enhances analytical tools for elliptic integrable systems.

## Abstract

We use generalized kernel functions to construct explicit solutions by integrals of the non-stationary Schr\"odinger equation for the Hamiltonian of the elliptic Calogero-Sutherland model (also known as elliptic Knizhnik-Zamolodchikov-Bernard equation). Our solutions provide integral represenations of elliptic generalizations of the Jack polyomials.