Localized Solitons of Hyperbolic su(N) AKNS System

Using the nonlinear constraint and Darboux transformation methods, the (m1, · · · ,mN ) 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 Ψy = JΨx + U(x, y, t)Ψ where J is constant real diagonal and U = −U . When different solitons move in different velocities, each component Uij of the solution U has at most mimj peaks as t → ∞. This corresponds to the (M,N) solitons for the DSI equation. When all the solitons move in the same velocity, Uij still has at most mimj peaks if the phase differences are large enough.