Novikov equation, as a cubic generaliztion of the celebrated Camassa-Holm equation, obeys several nontrivial properties. In this talk, we first study the integrability and invariant properties of the Novikov equation. It is shown that there is a Liouville correspondence between the Novikov hierarchies and Sawada-Kotera hierarchies. As a conclusion, an infinite number of conservation laws of the Novikov equation is derived. Second, we verify the non-smooth solitons are orbitally stable in the energy space by establishing the inequalities relating the maximum value of approximate solutions and Hamiltonian conservation laws. Finally, we study the integrability, structure of non-smooth solitons and their stability in the energy space of a two-component Novikov system.