Ring-like double-breathers in the partially nonlocal medium with different diffraction characteristics in both directions under the influence of external potential and gain/loss

Abstract

This study explores a (3+1)-dimensional variable-coefficient partially nonlocal coupled nonlinear Schrödinger (NLS) model, revealing its dimensional reduction to a (2+1)-dimensional constant-coefficient analog. This transformation yields analytical solutions that manifest as double-breathers with Hermite-Gaussian envelopes. Focusing on the dynamic characteristics of these double-breathers, the research emphasizes their ring-like or cylinder-like structures, particularly in systems with exponential diffraction and gain, along with constant-type chirp and phases. Key parameters, such as the radius parameter R and thickness parameter ω, significantly influence the size, shape, and structural intricacies of the double-breathers. Additionally, Hermite parameters p and n allow for the formation of layered structures along the z-axis, enriching the wave dynamics. The integration of gain or loss phenomena links theoretical insights with practical applications, enhancing the relevance of the findings in real-world scenarios.