Orbital stability of solitary waves and a Liouville-type property to the cubic Camassa-Holm-type equation (Q2077795)

The authors first introduce cubic Camassa-Holm (CH) type equation. Even though most of the generalizations of CH equation are quadratic, there are also cubic ones in the literature such as Novikov equation. The equation discussed in the paper has both quadratic and cubic nonlinearities endowed with nonlinear dispersions. That enriches the equation in terms of solitary wave types. They classify all the solitary waves vanishing at infinity. Providing the conserved quantities, they study the stability of solitary waves and prove orbital stability in \(H^1\). They end the paper by proving unique continuation property of the cubic CH-type equation.