Mathieu Progressive Waves

• 来源期刊: 理论物理通讯：英文版
• 学科: 工学
• 关键词: 圆柱坐标系 波动方程 分离变量 循环坐标 一般形式 集中模式 椭圆形 精确解
• 年，卷（期）: 2011,（10）
• 页码范围: 733-739
• 页数: 7页
• 分类号: O175.1|TM359.401
• 语种: 英文

摘要

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 eurvilinear 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.