Dark and antidark soliton pairs in nonlocal media

Key findings from this study

• The study identifies two distinct families of vector soliton pairs: fast solitons with same-polarity structures and slow solitons with mixed-polarity configurations.
• The authors demonstrate that polarity in each component depends on relative background densities and nonlinear coefficients.
• The research reveals that spatial nonlocal nonlinearity induces symmetry-breaking internal structure within multi-component solitons when characteristic velocities are upshifted.

Overview

This research investigates soliton formation in a one-dimensional two-component defocusing nonlinear Schrödinger system featuring nonlocal interactions. The model incorporates arbitrary intra- and inter-component nonlinearities along with a general symmetric nonlocal response kernel, enabling applications across nonlinear optics and Bose-Einstein condensates. The study focuses on the miscible regime where the uniform background remains modulationally stable. A multiscale expansion yields an effective Korteweg-de Vries equation that governs small-amplitude, long-wavelength excitations. The analytical framework identifies two distinct families of vector soliton pairs with varying velocities and polarity structures. Direct numerical simulations validate the asymptotic predictions and reveal how nonlocal nonlinearity induces symmetry-breaking internal structure within multi-component solitons.

Methods and approach

The authors employ a multiscale expansion technique to derive an effective Korteweg-de Vries equation from the two-component defocusing nonlinear Schrödinger system. The system features arbitrary intra- and inter-component nonlinearities along with a general symmetric nonlocal response kernel. Analysis concentrates on the miscible regime where the uniform background exhibits modulational stability. The miscibility parameter governs whether components mix or separate spatially. Direct numerical simulations verify the stability and accuracy of asymptotic predictions. The model applies to thermal optical media, nematic liquid crystals, plasmas, and binary Bose-Einstein condensates with long-range interactions.

Results

The analytical framework reveals two distinct families of vector soliton pairs. Fast solitons propagate at higher velocities and exhibit same-polarity structures in both components, appearing as either dark-dark or antidark-antidark configurations depending on nonlocality strength. Slow solitons represent a novel class of mixed-polarity solutions where one component is dark and the other antidark. The polarity of each component depends on relative background densities and the system's nonlinear coefficients.

Direct numerical simulations confirm the stability and accuracy of the asymptotic predictions. When characteristic velocities are upshifted, solitons of different polarities emerge within the same component. This behavior suggests that spatial nonlocal nonlinearity induces symmetry-breaking internal structure within multi-component solitons. The model accounts for nonlocal effects arising in thermal optical media, nematic liquid crystals, plasmas, and dipolar Bose-Einstein condensates where anisotropic interactions produce spatially extended nonlinear potentials.

Implications

The discovery of mixed-polarity soliton pairs advances understanding of nonlocal effects in multi-component nonlinear systems. The ability of nonlocal nonlinearity to induce symmetry-breaking within soliton structures opens pathways for engineering novel wave phenomena in optical and quantum systems. The dual families of fast and slow solitons provide distinct dynamical regimes that may support different information transmission or storage mechanisms in photonic devices and atomic systems.

Applications span thermal optical media, nematic liquid crystals, plasmas, and Bose-Einstein condensates with dipolar or long-range interactions. In thermal materials, heat diffusion creates effectively nonlocal refractive index changes that stabilize solitons and suppress collapse in higher dimensions. For binary condensates, the framework describes systems where particles exert long-distance forces, extending beyond simple pairwise delta-function interactions. The general symmetric response kernel and arbitrary nonlinearity coefficients enable the model to capture a broad range of physical scenarios, supporting experimental design and theoretical predictions across multiple platforms.

Scope and limitations

This summary is based on the study abstract and available metadata. It does not include a full analysis of the complete paper, supplementary materials, or underlying datasets unless explicitly stated. Findings should be interpreted in the context of the original publication.