Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Spherical waves in odd-dimensional space


Author: J. G. Kingston
Journal: Quart. Appl. Math. 46 (1988), 775-778
MSC: Primary 35L05; Secondary 35Q05
DOI: https://doi.org/10.1090/qam/973389
MathSciNet review: 973389
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Abstract: The general solution is given of the $ \left( {2N + 1} \right)$-dimensional wave equation with spherical symmetry, $ {u_{tt}} - {u_{xx}} - \frac{{2N}}{x}{u_x} = 0$, in terms of two arbitrary functions and their first $ N$ derivatives. Simple transformations then yield the general solutions to the Euler-Poisson-Darboux equation, $ {u_{xy}} + \frac{N}{{\left( {x + y} \right)}}\left( {{u_x} + {u_y}} \right) = 0$, for integer $ N$, and also the one-dimensional wave equation, $ {u_{tt}} - {c^2}{u_{xx}} = 0$, for certain variable wave speeds $ c\left( x \right)$.


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DOI: https://doi.org/10.1090/qam/973389
Article copyright: © Copyright 1988 American Mathematical Society


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