On multi-soliton solutions to the Heisenberg ferromagnetic spin chain equation in (2+1)-dimensions

TL;DR

This paper derives explicit multi-soliton solutions for the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation using a Riemann-Hilbert approach, providing new insights into nonlinear wave propagation in ferromagnetic systems.

Contribution

It introduces a Riemann-Hilbert framework to obtain multi-soliton solutions for the (2+1)-D HFSC equation, which is a novel analytical approach for this model.

Findings

Explicit multi-soliton solutions are constructed.

One- and two-soliton solutions are graphically analyzed.

The method provides a new way to study nonlinear waves in ferromagnetic chains.

Abstract

This paper concentrates on the Heisenberg ferromagnetic spin chain (HFSC) equation in (2+1)-dimensions modelling nonlinear wave propagation in ferromagnetic spin chain. A variable transformation is first employed to reduce the studied equation. And then an associated matrix Riemann-Hilbert problem is built on the real line through analyzing spectral problem of the reduced equation. As a consequence, solving the obtained matrix Riemann-Hilbert problem with the identity jump matrix, corresponding to the reflectionless, the general multi-soliton solutions to the HFSC equation in (2+1)-dimensions are acquired. Specially, the one- and two-soliton solutions are worked out and analyzed graphically.