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Jingqun Wang, Yingnan Zhang, Lixin Tian. NONLINEAR STABILITY OF BREATHER SOLUTIONS TO THE MODIFIED KDV-SINE-GORDON EQUATION[J]. Journal of Applied Analysis & Computation, 2022, 12(5): 2043-2056. doi: 10.11948/20220044
Citation: Jingqun Wang, Yingnan Zhang, Lixin Tian. NONLINEAR STABILITY OF BREATHER SOLUTIONS TO THE MODIFIED KDV-SINE-GORDON EQUATION[J]. Journal of Applied Analysis & Computation, 2022, 12(5): 2043-2056. doi: 10.11948/20220044
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NONLINEAR STABILITY OF BREATHER SOLUTIONS TO THE MODIFIED KDV-SINE-GORDON EQUATION

  • 1.

    School of Mathematics and Statistics, Changshu Institute of Technology, Jiangsu, Hu-shan Road, 215500, China

  • 2.

    School of Mathematical Sciences, Nanjing Normal University, Nanjing, Wen-yuan Road, 210023, China

  • Corresponding author: Email address: tianlx@ujs.edu.cn(L. Tian)
  • Fund Project: The authors were supported by the Natural Science Foundation for the Universities in Jiangsu Province (No. 21KJB110012)
    Abstract

  • In this work, we are concerned with the modified KdV-sine-Gordon (mKdV-sG) equation. Breather solutions of the mKdV-sG equation are derived via using simplified Hirota's bilinear method. Moreover, we construct a new Lyapunov functional to present nonlinear stability of breather solutions to the mKdV-sG equation.
    MSC: 35Q51, 35Q53
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