Mathieu Progressive Waves |
| |
Authors: | Andrei B Utkin |
| |
Institution: | ICEMS, Instituto Superior Técnico, Tecnical University of Lisbon, Av. Rovisco Pais 1, Lisbon 1049-001, Portugal |
| |
Abstract: | A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal curvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type. |
| |
Keywords: | wave equation Bateman transform progressive wave Mathieu function |
|
| 点击此处可从《理论物理通讯》浏览原始摘要信息 |
| 点击此处可从《理论物理通讯》下载免费的PDF全文 |
|