This work investigates the exact general analytical solution of the Rayleigh equation for multielectron bubbles in liquid helium using Kudryashov and Sinelshchikov’s method. We firstly obtain its first integral involving three negative exponential powers, then a specific Sundman transformation is proper established to transform it into an equation for the elliptic functions, and finally the analytical solution expressed by Weierstrass elliptic function is constructed appropriately. As applications, the derived analytical solution is used to test numerical algorithm, and also to construct the analytical expressions of the bubble oscillation period and the derivatives of the bubble radius. Further, the influence of the pressure on the helium is also discussed.

中文翻译：

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Kudryashov和Sinelshchikov求解液氦中多电子气泡径向振荡问题的方法

这项工作使用 Kudryashov 和 Sinelshchikov 方法研究了液氦中多电子气泡的瑞利方程的精确一般解析解。我们首先得到它涉及三个负指数幂的第一个积分，然后适当建立特定的Sundman变换将其转化为椭圆函数方程，最后适当构造Weierstrass椭圆函数表示的解析解。作为应用，导出的解析解用于测试数值算法，也用于构造气泡振荡周期和气泡半径导数的解析表达式。此外，还讨论了压力对氦气的影响。