# Stable parity-time-symmetric nonlinear modes and excitations in a derivative nonlinear Schrodinger equation

## TL;DR

This paper explores the behavior of nonlinear modes in a derivative nonlinear Schrödinger equation with PT-symmetric potentials, revealing stable solitons, semi-elastic interactions, and mode transitions across PT phases.

## Contribution

It introduces the analysis of stable nonlinear modes in a derivative nonlinear Schrödinger equation with PT-symmetric potentials, including mode excitation across PT phases.

## Key findings

- Stable bright solitons exist even in broken PT phases.
- Exact nonlinear modes maintain shape after semi-elastic interactions.
- Adiabatic parameter changes can induce mode transitions between PT phases.

## Abstract

The effect of derivative nonlinearity and parity-time- (PT-) symmetric potentials on the wave propagation dynamics is investigated in the derivative nonlinear Schrodinger equation, where the physically interesting Scarff-II and hamonic-Hermite-Gaussian potentials are chosen. We study numerically the regions of unbroken/broken linear PT-symmetric phases and find some stable bright solitons of this model in a wide range of potential parameters even though the corresponding linear PT-symmetric phases are broken. The semi-elastic interactions between exact bright solitons and exotic incident waves are illustrated such that we find that exact nonlinear modes almost keep their shapes after interactions even if the exotic incident waves have evidently been changed. Moreover, we exert the adiabatic switching on PT-symmetric potential parameters such that a stable nonlinear mode with the unbroken linear PT-symmetric phase can be excited to another stable nonlinear mode belonging to the broken linear PT-symmetric phase.