Abstract
The principal objective of this article is to construct new and further exact soliton solutions of the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation which investigates the nonlinear dynamics of magnets and explains their ordering in ferromagnetic materials. These solutions are exerted via the new extended FAN sub-equation method. We successfully obtain dark, bright, combined bright-dark, combined dark-singular, periodic, periodic singular, and elliptic wave solutions to this equation which are interesting classes of nonlinear excitation presenting spin dynamics in classical and semi-classical continuum Heisenberg systems. 3D figures are illustrated under an appropriate selection of parameters. The applied technique is suitable to be used in gaining the exact solutions of most nonlinear partial/fractional differential equations which appear in complex phenomena.