Orbital Stability of Double Solitons for the Benjamin-Ono Equation

In this paper we prove the orbital stability of double solitons for the Benjamin-Ono equation. In the case of the KdV equation, this stability has been proved in [17]. Parts of the proof given there rely on the fact that the Euler-Lagrange equations for the conserved quantities of the KdV equation are ordinary differential equations. Since this is not the case for the Benjamin-Ono equation, new methods are required. Our approach consists in using a new invariant for multi-solitons, and certain new identities motivated by the Sylvester Law of Inertia.