具有超高斯形式的新的对数幂非线性薛定谔方程
New logarithmic power nonlinear Schrödinger equations with super-Gaussons
AI总结：
该研究提出了一种新的对数幂非线性薛定谔方程，允许超高斯形局域解，并通过数值模拟探讨了其在非线性光学和凝聚态物理中的应用。
摘要：
我们介绍了一类新的非线性薛定谔方程，其非线性项为对数幂型，并允许精确的超高斯形局域解。所得到的静态态具有平坦顶部和尖锐边缘的轮廓，被称为超高斯体（super-Gaussons），类似于经典对数非线性薛定谔方程（log-NLS）中的高斯体。该模型称为对数幂非线性薛定谔方程（logp-NLS），由参数p≥1控制溶iton核心的平坦程度和衰减的尖锐程度。数学上，p在标准log-NLS（p=1）和随着p增加而更加平坦的轮廓之间插值，而物理上它控制底层对数幂压缩定律的刚性。所提出的方程被构造以允许超高斯静态态，并可以在广义压力定律框架下后验解释，从而扩展了log-NLS。我们通过数值模拟研究了一维空间中超高斯体的动力学，对于各种p值进行模拟，展示了该参数如何调节溶iton的内部结构及其碰撞动力学。因此，logp-NLS通过允许更广泛的局域态家族，扩展了标准log-NLS，这些态具有独特的结构和动力学特性，表明其在非线性光学、玻色-爱因斯坦凝聚体及相关非线性介质中的相关性。
英文摘要：
We introduce a new class of nonlinear Schrödinger equations with a logarithmic-power nonlinearity that admits exact localized solutions of super-Gaussian form. The resulting stationary states possess flat-top profiles with sharp edges and are referred to as super-Gaussons, in analogy with the Gaussian Gaussons of the classical logarithmic NLS (log-NLS). The model, which we call the logarithmic-power NLS (logp-NLS), is parameterized by an exponent $p\geq1$ that controls the degree of flatness of the soliton core and the sharpness of its decay. Mathematically, $p$ interpolates between the standard log-NLS ($p=1$) and increasingly flat-top profiles as $p$ increases, while physically it governs the stiffness of an underlying logarithmic-power compressibility law. The proposed equation is constructed so as to admit super-Gaussian stationary states and can be interpreted a posteriori within a generalized pressure-law framework, thereby extending the log-NLS. We investigate the dynamics of super-Gaussons in one spatial dimension through numerical simulations for various values of $p$, demonstrating how this parameter regulates both the internal structure of the soliton and its collision dynamics. The logp-NLS thus generalizes the standard log-NLS by admitting a broader family of localized states with distinctive structural and dynamical properties, suggesting its relevance for flat-top solitons in nonlinear optics, Bose-Einstein condensates, and related nonlinear media.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
