Dark, bright and other soliton solutions to the Heisenberg ferromagnetic spin chain equation

Abstract

In this study, the applications of the extended sinh-Gordon equation expansion method to a nonlinear Schrödinger equation that describes the nonlinear spin dynamics of (2 + 1)-dimensional Heisenberg ferromagnetic spin chains with bilinear and anisotropic interactions in the semiclassical limit is presented. We successfully construct dark, bright, combined dark-bright, singular and combined singular soliton solutions to this equation. We give the parametric conditions for the existence of valid soliton to each of the obtained solutions. We plot the 2D and 3D graphics to some of the obtained solutions. The reported results of this study may be helpful in explaining the physical meaning of the studied model.