Rational Solitons in the Parity-Time-Symmetric Nonlocal Nonlinear Schrödinger Model

Abstract

In this paper, via the generalized Darboux transformation, rational soliton solutions are derived for the parity-time-symmetric nonlocal nonlinear Schrödinger (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.

18 pages, 9 figures, 1 table

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Cited by in corpus (6)

• Multi-place nonlocal systems
• General stationary solutions of the nonlocal nonlinear Schrödinger equation and their relevance to the PT-symmetric system
• Rational solutions of the defocusing nonlocal nonlinear Schrodinger equation: Asymptotic analysis and soliton interactions
• Peregrine rogue waves in the nonlocal nonlinear Schrödinger equation with parity-time symmetric self-induced potential
• Curved wedges in the long-time asymptotics for the integrable nonlocal nonlinear Schrödinger equation
• Nonlocal reductions of the Ablowitz-Ladik equation