Orbital stability of two-component peakons

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