# Integrable nonlocal asymptotic reductions of physically significant nonlinear equations

## TL;DR

This paper derives integrable nonlocal asymptotic reductions from key nonlinear equations, revealing physical links between nonlocal integrable systems and important physical models like water waves and Klein-Gordon equations.

## Contribution

It introduces a novel connection between nonlocal integrable reductions of the AKNS system and physically significant nonlinear equations.

## Key findings

- Asymptotic approximations transform to the integrable AKNS system.
- Establishes physical relevance of nonlocal reductions like PT-symmetric equations.
- Links nonlocal integrable systems to classical nonlinear wave equations.

## Abstract

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.