Narrow Results

In this paper, we apply the method of dynamical systems to the traveling wave solutions of the Novikov equation. Through qualitative analysis, we obtain bifurcations of phase portraits of the traveling system and exact cuspon wave solution, as well as a family of breaking wave solutions (compactons). We find that the corresponding traveling system of Novikov equation has no one-peakon solution.

The Novikov equation is a generalization of the Camassa–Holm one. It models the propagation of unidirectional shallow water waves on a flat bottom. In this paper, we prove the well-posedness of $H^2$ and $H^3$ solutions of the Cauchy problem, associated with this equation.