论文标题
无粘性流体中欧拉方程和固定结构的溶液
Solutions of the Euler equations and stationary structures in an inviscid fluid
论文作者
论文摘要
研究了描述无粘性流体的二维稳定流的欧拉方程。这些方程将降低为流函数的一个方程，然后使用hirota函数，发现了三个非线性椭圆方程的溶液。 ％：Sine-Gordon，Sinh-Gordon和Tzitzéica。发现的解决方案被解释为旋转流体，喷气机，源和水槽的链，涡流结构中的来源。我们提出了一种新的简单方法，以椭圆函数的有理表达式构建解决方案。结果表明，在椭圆形sin-gordon方程的情况下，对封闭曲线的流体通量进行了量化。
The Euler equations describing two-dimensional steady flows of an inviscid fluid are studied. These equations are reduced to one equation for the stream function and then, using the Hirota function, solutions of three nonlinear elliptic equations are found. %: Sine-Gordon, Sinh-Gordon and Tzitzéica. The solutions found are interpreted as sources in a rotating fluid, jets, chains of sources and sinks, vortex structures. We propose a new simple method for constructing solutions in the form of rational expressions of elliptic functions. It is shown that the flux of fluid across a closed curve is quantized in the case of the elliptic Sin-Gordon equation.
