Abstract
In this paper we show that the standing waves of the form (e it u(x),e it u(x)), > 0, u(x) real and positive, are stable for the system i @u @t + uxx + (|u| 2p 2 + |v| p |u| p 2 )u = 0 i @v @t + vxx + ( |u| p |v| p 2 + |v| 2p 2 )v = 0 provided 2 p p 1 and two for 0 < < p 1 but it is stable in both cases.
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