Orbital Stability And Asymptotic Stability Of MKdV Breather-type Soliton Solutions

In recent years, the stability of mKdV breather-type soliton solutions problems are more and more attention in the field of the applied science and the scientific. A new form of mKdV equation is acquired with the help of a nonlinear transformation,considering this new equation to have a separated variables solution-breather-type soliton solutions. However, this kind of solution stability is fluctuation. In order to proof stability, we give stability tests for any breather. Therefore, finding the any breather-type soliton solutions satisfies a suitable nonlinear stationary equations,linear operator and new Lyapunov functional is our main work.In this paper, we study the stability of modified Korteweg-de Vries equation breather. By using variable separation method, we obtain the exact breather-type soliton solutions. Moreover, this kind of solutions are globally stable in H2 topology,and we describe a simple,mathematical proof of the orbital stability and asymptotic stability of breather-type soliton solutions under a class of small perturbation.In Chapter 1, we introduce the background of related research work and the research status, and summarize the main work of this paper.In Chapter 2, we give a detalied procedure to obtain breather-type soliton solutions by using variables separation method.In Chapter 3, we study breather-type profile with some properties.In Chapter 4 and 5, we devoted to prove Theorem 1.3.1 and 1.3.3 respectively.And conclusions and future work are summarized in Chapter 6.