Integrable nonlocal asymptotic reductions of physically significant nonlinear equations

Quasi-monochromatic complex reductions of a number of physically important equations arc obtained. Starting from the cubic nonlinear Klein-Gordon (NLKG), the Korteweg-de Vries (KdV) and water wave equations, it is shown that the leading order asymptotic approximation can be transformed to the well-known integrable AKNS system (Ablowitz et al 1974 Stud. Appl. Math. 53 249) 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 paritytime, reverse space-time and reverse time nonlocal nonlinear Schrodinger equations.