Geodesic
Solutions of ultrahyperbolic equations and their application in texture analysis
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 12, pp. 2159-2167 
T. I. Savyolova. Solutions of ultrahyperbolic equations and their application in texture analysis. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 12, pp. 2159-2167. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_12_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Solutions of ultrahyperbolic $2\times 2$ equations are examined. An inverse diffraction problem—the recovery of the orientation distribution function from x-ray or neutron measurements of pole figures (PFs)—is reduced to a system of integral equations on the rotation group $SO(3)$. By transforming $SO(3)$, the original problem is reduced to a well-known problem in integral geometry, namely, to the recovery of a function in three-dimensional space from known integrals along straight lines. Upon this transform, the PFs are solutions to an ultrahyperbolic equation and the solution is nonunique.

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