  Quasi-monochromatic complex reductions of a number of physically important
equations are obtained. Starting from the cubic nonlinear Klein-Gordon (NLKG),
the Korteweg-deVries (KdV) and water wave equations, it is shown that the
leading order asymptotic approximation can be transformed to the well-known
integrable AKNS system [6] associated with second order (in space) nonlinear
wave equations. This in turn establishes, for the first time, an important
physical connection between the recently discovered nonlocal integrable
reductions of the AKNS system and physically interesting equations. Reductions
include the parity-time, reverse space-time and reverse time nonlocal nonlinear
Schrodinger equations.
