Abstract
The system: $u_\xi = - zv$, $v_\xi = \bar zu$, $z_\tau = u\bar v - \gamma z$ with $z \to 0$ at $\tau \to - \infty $ and initial data for ${\bf u} = (u,v)$ at $\xi = 0$ are considered. Well posedness results are obtained for this and also for a version discretized in $\tau $. Stability is considered as $\xi \to \infty $.
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