Theoretical Studies On Nonlinear Localized Excitations In Quasi-one-Dimensional Ferromagnets With The Dzyaloshinskii-Moriya Interaction

In recent years,nonlinear localized waves containing solitons,breathers and rogue waves have received a great deal of studies due to their extensively theory and application values in many various fields ranging from solid state to hydrodynamics,plasma and nonlinear optical systems.On the basis of analyzing and summarizing the research status and theoretical research methods at home and abroad,this thesis focuses on theoretical studies on the dynamic behavior of nonlinear local waves in quasi-one-dimensional ferromagnetic systems.Especially,some meaningful results are obtained.The contents of thesis are as following:In chapter one,we introduce the development history of ferromagnetism and nonlinear dynamics in ferromagnets.What is more,we review the Dzyaloshinskii-Moriya interaction and the Heisenberg model and Landau-Lifshitz(LL)equation.Finally,we mention the relevant research methods containing the Hirota bilinear method,the Darboux transformation method and the quasi-discreteness approach.In chapter two,we study the propagation and interaction of magnetic solitons in a ferromagnetic thin film with the interfacial Dzyaloshinskii-Moriya interaction.In the long wave limit,the governing Landau-Lifshitz-Gilbert equation can be transformed into an integrable nonlinear Shr?dinger-type equation.By means of the Hirota bilinear method,the analytical expressions of one-,two-,and three-soliton solutions are obtained.Our results show that the Dzyaloshinskii-Moriya interaction can change the velocities of magnetic solitons and affect the colliding position of the two solitons.In addition,we find a reverse effect of the propagation direction of the magnetic soliton.In chapter three,we present a theoretical work on nonlinear localized excitations in a ferromagnetic thin film with an interfacial Dzyaloshinskii-Moriya interaction.Making use of the Generalized Darboux transformation,the analytical forms of magnetic breathers and the first-to third-order rogue wave solutions are exactly constructed.We find that the introduction of the Dzyaloshinskii-Moriya interaction can cause a reverse effect of the propagation direction of the magnetic breather,and varying the value of the Dzyaloshinskii-Moriya interaction parameter can change the velocity of the magnetic breather.Moreover,we show that first-to third-order magnetic rogue waves can rotate clockwise as the intensity of the Dzyaloshinskii-Moriya interaction increases.In chapter four,bright type nonlinear localized modes in an easy-axis weak ferromagnetic zigzag lattices containing next-nearest-neighbor couplings are analytically studied.By the use of a quasi-discreteness multiple-scale method,analytical forms of the bright nonlinear localized modes are constructed.The influence of the next-nearest-neighbor coupling on the Brillouin zone centre mode and boundary mode are respectively analyzed.Particularly,we observe a reversal effect of the speed direction of the Brillouin zone boundary mode.The last chapter is devoted to providing our concluding remarks.