A NEW INTEGRABLE SYSTEM - THE INTERACTING SOLITON OF THE BO

The interacting soliton equation of the Benjamin-One equation (BO) is found to be s(t) = Hs(xx) - cs(x) - is(x)H(s(-1)s(x))- is(-1)s(x)H(s(x )), where H is the Hilbert transform. It is integrable in the sense th at it has infinitely many commuting symmetries and conservation laws i n involution. Only solitons with speed specified by the spectral param eter c emerge from its time evolution. Since it is connected to the BO by the interacting soliton projection solutions can be obtained via d erivatives of solutions of the Benjamin-One equation, with respect to asymptotic phases.