Stationary Oscillations in a Damped Wave Equation from Isospectral Bessel Functions

Fredholm行列式解在修正KP层次和二维Toda晶格中的应用：等谱与非等谱约化

Fredholm determinant solutions to the modified KP hierarchy and 2D Toda lattice: isospectral and non-isospectral reductions

本文研究修正KP层次和二维Toda晶格的Fredholm行列式解，通过等谱约化构造了mKdV、修正Camassa-Holm和聚焦非线性薛定谔方程的解，并展示了非等谱约化得到变形Bessel行列式解。

三重球贝塞尔函数积分与指数和高斯阻尼：迈向解析的N点相关函数协方差模型

Triple-Spherical Bessel Function Integrals with Exponential and Gaussian Damping: Towards an Analytic N-Point Correlation Function Covariance Model

本文推广了递归方法，并提出了非递归方法，以解析计算带指数或高斯阻尼的三重球贝塞尔函数积分，结果用勒让德函数、伽马函数和超几何函数表示，为N点相关函数协方差建模提供工具。

贝塞尔核行列式与可积方程

Bessel kernel determinants and integrable equations

本文利用Its-Izergin-Korepin-Slavnov可积算子与Riemann-Hilbert方法，证明贝塞尔行列式点过程的乘性统计量满足描述Sturm-Liouville等谱形变的可积非线性偏微分方程，并建立其与Painlevé V型方程的联系及初值问题研究。

Green's functions and the Cauchy problem of the Burgers hierarchy and forced Burgers equation

We consider the Cauchy problem for the Burgers hierarchy with general time dependent coefficients. The closed form for the Green's function of the corresponding linear equation of arbitrary order $N$ is shown to be a sum of generalised hypergeometric functions. For suitably damped initial conditions we plot the time dependence of the Cauchy problem over a range of $N$ values. For $N=1$, we introduce a spatial forcing term. Using connections between the associated second order linear Schrödinger and Fokker-Planck equations, we give closed form expressions for the corresponding Green's functions…