Conserved quantities along with Painlevé analysis and optical solitons for the nonlinear dynamics of Heisenberg ferromagnetic spin chains model

In this paper, we will investigate a famous model of nonlinear sciences namely [Formula: see text]-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 Painlevé test will also be studied in this paper.