Research Of The Soliton In A One-Dimensional Ferromagetic Ring With The Hirota's Method

With the development of science and technology, Condensed Matter Physics hasbecome the most important and abundant branch study of modern physics. Fruitfulefforts have been worked out by mass of researchers, which infiltrated rapidly withother studies and made great effect to the development of technology. Studies ofone-dimensional system, especially aspects of one-dimensional ferromagnetic chainand ionic crystal, have been the hottest topics in the studying field, which causedmore and more concerns by physical theoreticians and researchers. As is known to all,studies of one-dimensional problem could be concluded as solving nonlinearevolution equations. Compared to general linear equations which always had propersolutions, lots of difficulties existed when solving nonlinear equations. Differentnonlinear equations requested for different methods, a certain solution was onlysuitable for exact types of such equations. According to a certain type of nonlinearequation, when it happened to increase or reduce nonlinear terms, solutions could betotally different. As a result, how to get exact solutions was said very important to thestudies of nonlinear problems. Upon now, practical solving methods include Inversescattering methods, the method of traveling wave solution, and Multiple scalemethods etc. This article is creative using a new method-Hirota Method-to solvethe improve-nonlinear Schrodinger equation under one-dimensional ferromagneticchain model, one-soliton solution has already been worked out by the method oftraveling wave solution by other physical scientise. In contrast, this paper introducesthe method taking advantage of Hirota method, to work out one-soliton solution to theimprove-nonlinear Schrodinger equation. At the same time, it compares to result ofother articles.We try to calculate a mathematic two-soliton solution model. However,the complexity of physical two-soliton solution model, which is reflected by differentunknown parameters as well as uncompleted two-soliton solution structure, limits theaccuracy to the mentioned equation solution. Nevertheless, its study of multi-solitonsolution gives wide space to further researches.This article is consisted by the foreword and five chapters. Foreword tells the historical meanings to this studying theme, it also summarizes several studyingtheories as well as efforts related to the specific theme.Chapter 1: We bring the background of soliton solution in by solving differentnonlinear equations, soliton's definition and characteristics are introduced.Chapter 2: We show the physical model of one-dimensional ferromagnetic chain.Improve-nonlinear Schrodinger equation is also obtained under the A-B effect.Chapter 3: Firstly We give introduction on a new method in solving nonlinearequations-Hirota Method, then stress on how to take advantage of Hirota Method.The definition and character would be also introduced in this chapter.Chapter 4: We figure the new Hirota Method, in solving improve-nonlinearSchrodinger equation of one-dimensional ferromagnetic chain and work out theone-soliton solution and two-soliton solution.Chapter 5: We make conclusions on solving improve-nonlinear Schrodingerequation via Hirota Method and discuss aiming at its advantages and disadvantagesspread at the same time. It finally gives general summary and practical expectation tothis paper.