Wave patterns of (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chains in the semiclassical limit

Abstract

A special kind of nonlinear Schrödinger equation (NLSE) with conformable fractional derivative is considered. And via the complete discrimination system for polynomial method, all the single traveling wave solutions are presented, especially the soliton solutions, which are very important in describing the Heisenberg ferromagnetic spin chains. Moreover, to see the fractionalize effects clearly, numerical simulations are conducted and corresponding graphs are also plotted. The results in this paper include all the solutions in the existing literatures, and some solutions, such as elliptic functions solutions, are initially shown. From those results we can see certain wave propagation patterns of the aforementioned model, for example, the soliton and double periodic propagation patterns, which would be helpful for us to understand this model more clearly and could even shed light on the further analysis of the nonlinear properties of magnetic materials.