Authors: Sergey V. Ershkov
A new type of exact solution of the reduced 3 dimensional spatial PWE (paraxial wave equation) for the case of bipolar coordinates is presented here. First, we consider a self-similar representation of the solution in a bipolar coordinate system, the second we additionally reduce PWE under a proper paraxial assumption. Analyzing the structure of the final equation, we obtain the simple exact solution which is proved to satisfy to such an equation in bipolar coordinates. Besides, there is a limitation of the components of self-similar solution of a new type.
Comments: 5 Pages. Keywords: Helmholtz equation, PWE, paraxial approximation, bipolar coordinates
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[v1] 2013-03-01 15:56:25
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