Integrable nonlocal asymptotic reductions of physically significant nonlinear equations. (21st March 2019)

• Record Type: Journal Article
• Authors: Ablowitz, Mark J; Musslimani, Ziad H
• Is Part Of: Journal of physics. Volume 52:Number 15(2019)
• Publication Date: 2019-03-21
• Subjects: integrable systems -- nonlinear waves -- solitons and inverse scattering transform -- nonlinear Schrödinger equation; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ab0e95
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: Quasi-monochromatic complex reductions of a number of physically important equations are 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 parity-time, reverse space-time and reverse time nonlocal nonlinear Schrödinger equations.