Mathieu Progressive Waves

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 c...

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Bibliographic Details
Published inCommunications in theoretical physics Vol. 56; no. 10; pp. 733 - 739
Main Author Utkin, Andrei B
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.10.2011
Subjects
Constraining
Cylindrical coordinates
Eccentricity
Exact solutions
Feasibility
Mathematical analysis
Mathematical models
Transforms
一般形式
分离变量
圆柱坐标系
循环坐标
椭圆形
波动方程
精确解
集中模式
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Summary: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.
Bibliography:wave equation, Bateman transform, progressive wave, Mathieu function
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.
11-2592/O3
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0253-6102
DOI:10.1088/0253-6102/56/4/23