Integrable space-time shifted nonlocal nonlinear equations

In 1974 Ablowitz, Kaup, Newell, Segur (AKNS) put forward a theoretical framework whereby one can construct evolution equations that are (i) integrable in the sense of existence of infinite number of conservation laws and (ii) solvable by the inverse scattering transform. In subsequent years, many physically important integrable evolution equations were identified and the focus of the subject shifted towards methods to find special solutions and enhancing the underlying analysis. The discovery of a new reduction of the original AKNS system and the PTsymmetric integrable nonlocal nonlinear Schrodinger (NLS) equation more than forty years later was surprising. Subsequently, additional nonlocal integrable reductions were found allowing nonlocality to be manifested in the time domain as well. This paper reports on yet another novel set of integrable reductions for the original AKNS system and associated new space-time nonlocal NLS type equations with space and time shifts. Integrability and inverse scattering transform are established along with soliton solutions. Their unique properties are discussed along with detailed comparison with the respective standard (non shifted) PTand reverse space-time symmetric NLS equations. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

The AKNS theoretical framework introduced integrable evolution equations solvable by the inverse scattering transform, leading to the discovery of many physically important integrable equations. Subsequent research focused on finding special solutions and enhancing analysis methods. Surprisingly, new reductions and integrable nonlocal NLS equations were discovered after forty years, with additional nonlocal reductions allowing manifestation in the time domain. This paper reports on novel integrable reductions for the AKNS system, space-time nonlocal NLS equations, and soliton solutions.