Study On The Solitons In One-dimensional Ferromagnetic Systems

Nonlinear phenomena in one-dimensional magnetic systems have attractedconsiderable attention since 1931. And the researches took on great practicalsignificances especially when great progress of soliton excitations in one-dimensionalmagnets had been made both in experimental and theoretical studies in the later1970's. Presently, problems of soliton excitations in low-dimensional magneticmaterials are one of the hot topics in theoretical and experimental studies in the fieldof condensed physics.The work of this thesis mainly concentrates on the nonlinear excitations in aquasi-one-dimensional ferromagnetic chain, and the main results obtained are asfollows:(1) Cnoidal wave, envelope soliton and kink soliton solutions are obtained underdifferent anisotropic conditionsDue to a variety of physical properties, magnets can exhibit various types ofnonlinear localized excitations, such as domain walls, magnetic rotation waves, andmagnetic solitons. There may be different types of nonlinear excitations withdissimilar physical properties in different cases of anisotropy. Therefore, aone-dimensional ferromagnetic chain with various types of anisotropy, which includeexchange anisotropy, single-ion anisotropy, and next nearest-neighbor interaction, wasconsidered in this thesis. Some types of cnoidal waves and two kinds of solitons,envelope solitons and kink solitons, are obtained, and the influence of single-ionanisotropy and next nearest-neighbor interaction on cnoidal waves and solitons arediscussed, respectively. The results indicate that single-ion anisotropy makes thecnoidal waves and solitons to excite easily in an easy-plane ferromagnetic chain butdifficultly in an easy-axis one, and makes them more stable in the easy-axisferromagnetic chain but less stable in the easy-plane one. Moreover, nextnearest-neighbor interaction makes for the stability of solitons, especially when G/J＜1.(2) Modified nonlinear Schr6dinger equations reduced from the systems underconsideration in this thesis are resolved by travelling wave method and multiple scalesmethod without a great deal of calculation.The dynamical equation of nonlinear excitations in a one-dimensionalferromagnetic chain is nonlinear Schrodinger equation (NLS) in general. Someapproaches, such as inverse scattering method, multiple scales method, Hirota method,and travelling wave method, are usually used to resolve NLS equations. However, theequations obtained in a certain distinct case are usually more complex than thestandard NLS equation; hence the methods available might be different as before, andmost of them are complex, with a large amount of calculation. The equations ofmotion obtained in this thesis are modified NLS equations which can be resolved bytwo simple methods, travelling wave method and multiple scales method, and somemeaningful results are obtained.