论文标题
标量klein-戈登方程及其分析持续的分散图
Scalar Klein--Gordon equation and its analytically continued dispersion diagram
论文作者
论文摘要
标量klein-gordon方程描述了带有截止的波导中的波动运动。例如，可以通过标量klein-gordon方程来描述将弹性线锚定在实心底座上的弹性绳的位移。我们使用分析图的分析延续概念分析了该方程。特别是，表明色散图在拓扑上等同于分析嵌入在二维复合空间中的管。使用Cauchy的定理在此管子上研究了相应的傅立叶积分。标量klein-gordon方程的基本属性已建立。
The scalar Klein-Gordon equation describes wave motion in a waveguide with a cut-off. For example, the displacement of an elastic cord anchored to a solid base by elastic elements can be described by the scalar Klein-Gordon equation. We analyse this equation using the concept of analytical continuation of dispersion diagram. Particularly, it is shown that the dispersion diagram is topologically equivalent to a tube analytically embedded in two-dimensional complex space. The corresponding Fourier integral is studied on this tube using the Cauchy's theorem. The basic properties of the scalar Klein-Gordon equation are established.
