Orbital stability of two-component peakons

We prove that the two-component peakon solutions are orbitally stable in the energy space.The system concerned here is a two-component Novikov system,which is an integrable multi-component extension of the integrable Novikov equation.We improve the method for the scalar peakons to the two-component case with genuine nonlinear interactions by establishing optimal inequalities for the conserved quantities involving the coupled structures.Moreover,we also establish the orbital stability for the train-profiles of these two-component peakons by using the refined analysis based on monotonicity of the local energy and an induction method.