The article describes new linear dislocations, revealing integration properties in elastic mediums, suggesting broader implications in geometric defect theory.
The article describes new types of linear dislocations in an elastic medium within the framework of the geometric theory of defects. All locally flat separable metrics in three-dimensional space are found that admit two Killing vector fields and one second rank Killing tensor. The obtained metrics have important property: the variables in the corresponding Hamilton-Jacobi equation for geodesics are completely separable which leads to Liouville integrability of geodetic equations.
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Katanaev et al. (2026) studied this question.
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