Stability in the energy space of the sum of $ N $ solitary waves for an equation modelling shallow water waves of moderate amplitude

Abstract

<p style='text-indent:20px;'>Considered herein is an equation modelling the propagation of surface waves of moderate amplitude in shallow water regime, which admits blow-up solutions and solitary waves. Using modulation argument, combining the result of the stability of a single solitary wave with a property of almost monotonicity of local energy norm, we show that the decoupled sum of <inline-formula><tex-math id="M2">\begin{document}$ N $\end{document}</tex-math></inline-formula> solitary waves is orbitally stable in the energy space <inline-formula><tex-math id="M3">\begin{document}$ H^1({{\mathbb{R}}}) $\end{document}</tex-math></inline-formula>.</p>