Orbital stability and asymptotic stability of mKdV breather-type soliton solutions

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• 作者：Juan Wang ; Lixin Tian ; ^{tianlixin@njnu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; ^{tianlx@ujs.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Yingnan Zhang
• 关键词：mKdV equation ; Breather-type soliton solution ; Variable separation ; Orbital stability ; Asymptotic stability
• 刊名：Communications in Nonlinear Science and Numerical Simulation
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：45
• 期：Complete
• 页码：1-12
• 全文大小：1389 K

文摘

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.