Three types of Darboux transformation and general soliton solutions for the space-shifted nonlocal [formula omitted] symmetric nonlinear Schrödinger equation

Abstract

Under investigation is the space-shifted nonlocal PT symmetric nonlinear Schrödinger (NLS) equation, which is a novel nonlocal reduction of the classical AKNS system proposed by Ablowitz and Musslimani (2021). We construct three types of Darboux transformation with the help of the symmetry conditions of the linear matrix spectral problem. Several kinds of analytical solutions such as the periodic, breather-like and bounded soliton solutions under the zero background are derived from three kinds of spectral configurations on the complex plane. Dynamics of these solutions to the space-shifted nonlocal PT symmetric NLS equation are shown.