Exact soliton solution of Spin Chain with a external magnetic field in linear wave background

TL;DR

This paper derives exact multi-soliton solutions for an anisotropic spin chain under an external magnetic field within a linear wave background, analyzing their properties and stability criteria.

Contribution

It introduces a straightforward Darboux transformation method to construct explicit N-soliton solutions for the spin chain model with external magnetic field.

Findings

Explicit one- and two-soliton solutions are obtained and analyzed.

The dispersion law, effective soliton mass, and energy are characterized.

Soliton stability depends on anisotropic parameters and linear wave amplitude.

Abstract

Employing a simple, straightforward Darboux transformation we construct exact N-soliton solution for anisotropic spin chain driven by a external magnetic field in linear wave background. As a special case the explicit one- and two-soliton solution dressed by the linear wave corresponding to magnon in quantum theory is obtained analytically and its property is discussed in detail. The dispersion law, effective soliton mass, and the energy of each soliton are investigated as well. Our result show that the stability criterion of soliton is related with anisotropic parameter and the amplitude of the linear wave.