Kingston, J. G. Spherical waves in odd-dimensional space. (English) Zbl 0684.35063 Q. Appl. Math. 46, No. 4, 775-778 (1988). The author gives the general solution of the \((2n+1)\)-dimensional wave equation with spherical symmetry \[ u_{tt}-u_{xx}+(2n/x)u_x=0, \quad n \text{ is an integer}, \] in terms of two arbitrary functions and their first \(n\) derivatives. Transformations then yield the general solutions to the Euler-Poisson-Darboux equation \[ u_{xy}- (n/(x+y))(u_x+u_y)=0 \] and the one-dimensional wave equation \[ u_{tt}-x^{4n/(2n+1)}u_{xx}=0. \] Reviewer: Manfred Schneider (Karlsruhe) MSC: 35L05 Wave equation 35C05 Solutions to PDEs in closed form 35Q05 Euler-Poisson-Darboux equations Keywords:general solution PDFBibTeX XMLCite \textit{J. G. Kingston}, Q. Appl. Math. 46, No. 4, 775--778 (1988; Zbl 0684.35063) Full Text: DOI