Abstract
<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. </abstract>
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