Abstract
In this paper, we will investigate a famous model of nonlinear sciences namely (2 + 1)-dimensional nonlinear spin dynamics of Heisenberg ferromagnetic spin chains (HFSC) model for the evaluation of optical travelling waves by implementing unified method (UM). We will extract dark as well as bright solitary waves along with elliptic waves. We will draw conserved quantities of our governing model by utilizing dilation symmetry. At the end, the integrability of nonlinear spin dynamics of HFSC model with the help of Painleve test will also be studied in this paper.