Analytical Study On The Heisenberg Spin Chain Equation With Vatiable Coefficients

Heisenberg spin chain equation is a kind of very important model to describe ferromagnetic dynamics.This thesis is devoted to analytical solutions of the following Heisenberg equation with spin-transfer torque.Firstly,with the aids of Lax pair and Darboux transformation,we find some novel analytical solutions.Especially,we get the rogue wave solutions.Secondly,by use of the Jacobian elliptical functions,we obtain a class of solutions by a direct ansatz.Our results are helpful to understand how the spin-spin action and the spin-transfer torque to affect the properties of ferromagnet.The Heisenberg spin chain system is very important integrable equations and have been paid more attention.The traveling wave solution of the spin chain system is found by using the undetermined coefficient method.Based on the equivalence between the Heisenberg spin chain system and the nonlinear Schrodinger equation,the single soliton solution is solved by using AKNS system.Finally,the Hasimoto transform is used to solve the geometric surface of the Heisenberg spin chain system,so as to study the geometric properties of the surface.