# Dynamics of higher-order rational solitons for the nonlocal nonlinear Schrodinger equation with the self-induced parity-time-symmetric potential

## TL;DR

This paper investigates higher-order rational solitons in a nonlocal nonlinear Schrödinger equation with parity-time symmetry, revealing complex wave structures and their dynamics through analytical and numerical methods.

## Contribution

It introduces a nonlocal Darboux transformation to construct higher-order rational solitons for the nonlocal NLS equation with PT-symmetry, expanding understanding of their structures and behaviors.

## Key findings

- Rich wave structures depending on parameter choices
- Higher-order rational solitons exhibit diverse interactions
- Numerical simulations show stability under small noise

## Abstract

The integrable nonlocal nonlinear Schrodinger (NNLS) equation with the self-induced parity-time-symmetric potential [Phys. Rev. Lett. 110 (2013) 064105] is investigated, which is an integrable extension of the standard NLS equation. Its novel higher-order rational solitons are found using the nonlocal version of the generalized perturbation (1, N-1)-fold Darboux transformation. These rational solitons illustrate abundant wave structures for the distinct choices of parameters (e.g., the strong and weak interactions of bright and dark rational solitons). Moreover, we also explore the dynamical behaviors of these higher-order rational solitons with some small noises on the basis of numerical simulations.