The two-soliton of the cubic modified Camassa-Holm equation is nonlinearly stable under H^2 perturbations of the momentum variable.
Fokas, The Korteweg-de Vries equation and beyond, Acta Appl
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Stability of 2-soliton solutions for the modified Camassa-Holm equation with cubic nonlinearity
The two-soliton of the cubic modified Camassa-Holm equation is nonlinearly stable under H^2 perturbations of the momentum variable.