Linear stability analysis and spatial solitons in the one-dimensional and the two-dimensional generalized nonlinear Schrodinger equation with third-order dispersion and PT-symmetric potentials

In this paper, the existence and stability of the nonlinear spatial localized modes have been investigated for both self-focusing and self-defocusing in the nonlinear Schrodinger (NLS) equation with interplay of third-order dispersion (TOD), momentum term and complex parity-time (PT)-symmetric Scarf potential. The impact of the TOD and momentum coefficients on the regions of unbroken/broken linear PT symmetric phases has been studied numerically. For the nonlinear case, exact analytical expressions of the localized modes are obtained, respectively, in one- and two-dimensional nonlinear Schrodinger equation with TOD and momentum coefficients. The effects of both TOD and momentum term on the stability/instability structure of these localized modes have also been discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. It was found that the relative strength of the TOD and momentum coefficients can utterly change the direction of the power flow which may be used to control the energy exchange among gain or loss regions.

Automated summary

This paper investigates the existence and stability of nonlinear spatial localized modes in the NLS equation with the interplay of TOD, momentum term, and complex PT-symmetric Scarf potential. Numerical studies show the impact of TOD and momentum coefficients on the linear PT symmetric phases. Analytical expressions of localized modes are obtained in one- and two-dimensional NLS equations with TOD and momentum coefficients. The study discusses how the relative strength of TOD and momentum coefficients can alter the power flow direction, consequently affecting energy exchange control.