具有李-黄-杨修正的扩展广义彭罗斯方程中的二维孤子
Two-dimensional solitons in extended GPE models with Lee-Huang-Yang corrections
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中文总结 AI 辅助
研究扩展广义彭罗斯方程中二维孤立波，用多尺度渐近方法推导有效模型，构建多种孤子近似解析解，通过数值模拟监测其动力学稳健性，揭示了平均场和量子涨落竞争模型中的多维孤子解。
中文摘要 AI 辅助
我们研究了由具有对数平均场和李-黄-杨相互作用的扩展格罗斯-皮塔耶夫斯基方程描述的量子液滴环境中二维孤立波的存在性和动力学。在背景调制稳定区域，我们采用合适的多尺度渐近方法推导出与卡多姆采夫-彼得维谢夫斯基方程和戴维-斯图尔特森方程对应的有效非线性可积模型。基于这些简化模型，我们构建了描述线孤子、代数局域化块状孤子、环形孤子和指数局域化瞬子的近似解析解，并通过数值模拟监测这些解的动力学稳健性。结果揭示了在平均场和量子涨落竞争模型中前所未有的多维孤子解，适用于当前的超冷原子实验。
英文摘要
We investigate the existence and dynamics of two-dimensional solitary waves in a quantum droplet environment described by the extended Gross-Pitaevskii equation featuring logarithmic mean-field and Lee-Huang-Yang interactions. In the modulationally stable regime of the background, we employ suitable multiscale asymptotic methods to derive effective nonlinear integrable models corresponding to the Kadomtsev-Petviashvili and Davey-Stewartson equations. Based on these reduced models, we construct approximate analytical solutions describing line solitons, algebraically localized lump solitons, ring solitons, and exponentially localized dromions embedded on the droplet background. The dynamical robustness of these solutions is monitored through numerical simulations. Line, lump and ring solitons stay closest to the theoretical predictions, although progressively deviate due to the emergence of small-amplitude radiation, while dromions depart from their analytical waveform the most, although they roughly maintain their shape. Our results unveil unprecedented multidimensional soliton solutions in models featuring the competition of mean-field and quantum fluctuations and as such are amenable to current ultracold atom experiments.
