Dark solitons of the Gross-Neveu model

TL;DR

This paper derives explicit N-soliton solutions for the classical (1+1)-dimensional Gross-Neveu model with non-zero boundary conditions, using a direct method based on the Cauchy matrix approach.

Contribution

It introduces a novel method to construct multi-soliton solutions for the Gross-Neveu model with non-zero boundary conditions.

Findings

Explicit N-soliton solutions are obtained.

Solutions satisfy non-zero boundary conditions.

Method leverages properties of soliton matrices in the Cauchy matrix framework.

Abstract

We present N-soliton solutions for the classical (1+1)-dimensional Gross-Neveu model which satisfy non-zero boundary conditions. These solutions are obtained by direct method using some properties of the soliton matrices that appear in the framework of the Cauchy matrix approach.