Wang Jingqun, from the School of Mathematics and Statistical Mathematics recently published the title "Nonlinear stability of breather solutions to the coupled modified Korteweg-de Vries equations" in the internationally renowned journal "Communications in Nonlinear Science and Numerical Simulation" (Applied Mathematics, Chinese Academy of Sciences, IF = 4.115) with the first author and Changshu Institute of Technology as the first completion unit ". This study reported the cmKdV equations. A new Lyapunov function is constructed via the conservation laws. Furthermore, this paper presents the details of the nonlinear stability of the cmKdV breather solutions via a minimization problem of the variational characterization of the first eigenvalue.. Thesis link:

https://www.sciencedirect.com/science/article/abs/pii/S1007570420301994

Paper Title：Nonlinear stability of breather solutions to the coupled modified Korteweg-de Vries equations

Journal：Communications in Nonlinear Science and Numerical Simulation

Abstract：This paper is concerned with the coupled modified Korteweg-de Vries (cmKdV) equations. We derive infinite conservation laws through the Lax pair of the cmKdV equations. Through the analysis of the spectral stability with the conservation laws, we obtain the nonlinear stability of breather solutions to the cmKdV equations.

Wang Jingqun was once a teacher of Deapartment of Information and Computing Science, Changshu Institute of Technology. She received her PhD degree in 2019 from Nanjing Normal University (China). Her current research interests focus on the rogue wave solutions, including stability of breathers and numerical analysis of soliton solutions.