Rational Solitons in the Parity-Time-Symmetric Nonlocal Nonlinear Schr\"{o}dinger Model

TL;DR

This paper derives and analyzes rational soliton solutions in a parity-time-symmetric nonlocal nonlinear Schrödinger model, revealing unique interaction behaviors and stability properties of these solutions.

Contribution

It introduces a generalized Darboux transformation approach to find rational solitons in a nonlocal PT-symmetric NLS model, including first- and second-order solutions with novel interaction features.

Findings

First-order solutions show elastic interactions without phase shifts.

Second-order solutions exhibit complex near-field interactions with peak-valley structures.

Numerical stability analysis confirms the robustness of the rational solitons.

Abstract

In this paper, via the generalized Darboux transformation, rational soliton solutions are derived for the parity-time-symmetric nonlocal nonlinear Schr\"{o}dinger (NLS) model with the defocusing-type nonlinearity. We find that the first-order solution can exhibit the elastic interactions of rational antidark-antidark, dark-antidark, and antidark-dark soliton pairs on a continuous wave background, but there is no phase shift for the interacting solitons. Also, we discuss the degenerate case in which only one rational dark or antidark soliton survives. Moreover, we reveal that the second-order rational solution displays the interactions between two solitons with combined-peak-valley structures in the near-field regions, but each interacting soliton vanishes or evolves into a rational dark or antidark soliton as $|z|\ra \infty$. In addition, we numerically examine the stability of the first- and second-order rational soliton solutions.