多面体Lane-Emden方程的对称约化

On the solutions of the critical Lane-Emden equation in higher space dimensions

In this paper we study solutions of the critical Lane-Emden equation in higher space dimensions. We show that after certain transformations the general solution can be written in terms of elliptic functions. We restrict ourselves to real solutions which can be used in physical applications.

关于兰金-埃蒙德不等式稳定性估计

Stability estimate for the Lane-Emden inequality

本文研究了兰金-埃蒙德不等式稳定性估计，通过优化器流形的距离来提供余项估计。

液体Lane-Emden星的线性稳定性

Linear Stability of liquid Lane-Emden stars

本文研究了液体Lane-Emden星在径向扰动下的线性稳定性，发现稳定性依赖于参数$\gamma$和中心密度，并给出了相应的稳定与不稳定判据。

n = 5 Lane-Emden方程的所有解

All solutions of the n = 5 Lane-Emden equation

用Jacobian椭圆函数和Weierstrass椭圆函数得到了n = 5的Lane-Emden方程的所有实解。找到了一族新的解，它用非常简单的公式表示，只涉及雅可比椭圆函数。讨论了这些新解的一般性质和离散标度对称性。我们还评论了它们的可能应用。

Perturbed Lane-Emden equations as a boundary value problem with singular endpoints

The paper presents the solution for the existence of analytic solutions for some generalized Lane-Emden (LE) equation. Such solutions exists on the unit interval, which endpoints are singularities of the proposed perturbed LE equation. The solution has many possible applications and one of the examples was provided.

Stability analysis of orbital modes for a generalized Lane-Emden equation

We present a stability analysis of the standard nonautonomous systems type for a recently introduced generalized Lane-Emden equation which is shown to explain the presence of some of the structures observed in the atomic spatial distributions of magnetically-trapped ultracold atomic clouds. A Lyapunov function is defined which helps us to prove that stable spatial structures in the atomic clouds exist only for the adiabatic index $γ=1+1/n$ with even $n$. In the case when $n$ is odd we provide an instability result indicating the divergence of the density function for the atoms. Several numeric…