Localized solitons of the hyperbolic su( N ) AKNS system

Abstract

Using the nonlinear constraint and Darboux transformation methods, the localized solitons of the hyperbolic su(N) AKNS system are constructed. Here `hyperbolic su(N)' means that the first part of the Lax pair is where J is constant real diagonal and . When different solitons move in different velocities, each component of the solution U has at most peaks as . This corresponds to the solitons for the DSI equation. When all the solitons move in the same velocity, still has at most peaks if the phase differences are large enough.