Degenerate and non-degenerate solutions of [formula omitted]-symmetric nonlocal integrable discrete nonlinear Schrödinger equation

Abstract

In this paper, we explore the dynamics of degenerate and non-degenerate solutions of the PT-symmetric nonlocal integrable discrete nonlinear Schrödinger equation (ID-NLSE). Darboux transformation is applied to the associated linear eigenvalue problem also known as Ablowitz-Ladik (AL) scheme, and higher order non-trivial solutions are expressed in terms of ratio of the determinants. We use the Taylor series expansion to generates higher order degenerate soliton and breathing solutions. The determinant formula also enables to calculate the non-degenerate solution of PT-symmetric nonlocal ID-NLSE. Under the continuum limit one can easily recover the degenerate and non-degenerate solutions of PT-symmetric nonlocal NLSE.