New solitons and periodic wave solutions for the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation

Abstract

We consider a nonlinear Schrödinger type equation in (2+1) dimensions. The proposed equation describes the nonlinear spin dynamics of (2+1)-dimensional Heisenberg ferromagnetic spin chains with bilinear and anisotropic interactions in the semiclassical limit. We first construct three families of exact periodic solutions expressed in terms of Jacobi’s elliptic functions cn, sn and dn. We second consider the limit where the elliptic modulus approaches 1 to obtain bright and dark soliton solutions. Furthermore, we find a new type of soliton-like solution, illustrating the potentially rich set of wave solutions of the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation. Parametric conditions for the existence and uniqueness of exact solutions are presented. The derived structures of the obtained solutions offer a rich platform to study the nonlinear spin dynamics in magnetic materials.