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Elliptical, hyperbolic and parabolic dislocations.

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Title: Elliptical, hyperbolic and parabolic dislocations.
Authors: Katanaev, M. O.1 (AUTHOR) katanaev@mi-ras.ru, Mark, A. V.2 (AUTHOR) am-83-45@yandex.ru
Source: International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Applied Physics. 2/20/2026, Vol. 40 Issue 5, p1-21. 21p.
Subjects: Dislocation structure, Elastic solids, Hamilton-Jacobi equations, Dislocations in crystals
Abstract: The paper discusses dislocations in an elastic medium within the geometric theory of defects. All locally flat separable metrics in three dimensions are found. They describe dislocations that occur by cutting (inserting) a wedge, ellipsoid, hyperboloid or paraboloid of rotation and elliptical, hyperbolic or parabolic cylinders with subsequent gluing of the formed edges. The obtained dislocations have an important property: variables in the corresponding Hamilton–Jacobi equation for geodesics are completely separable resulting in the Liouville integrability of geodesic equations. In addition, variables in the Laplace equation also admit complete separation of variables. To our knowledge, elliptic, hyperbolic and parabolic dislocations are described for the first time. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Applied Physics is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 191456561
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Elliptical, hyperbolic and parabolic dislocations.
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  Data: <searchLink fieldCode="DE" term="%22Dislocation+structure%22">Dislocation structure</searchLink><br /><searchLink fieldCode="DE" term="%22Elastic+solids%22">Elastic solids</searchLink><br /><searchLink fieldCode="DE" term="%22Hamilton-Jacobi+equations%22">Hamilton-Jacobi equations</searchLink><br /><searchLink fieldCode="DE" term="%22Dislocations+in+crystals%22">Dislocations in crystals</searchLink>
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  Data: The paper discusses dislocations in an elastic medium within the geometric theory of defects. All locally flat separable metrics in three dimensions are found. They describe dislocations that occur by cutting (inserting) a wedge, ellipsoid, hyperboloid or paraboloid of rotation and elliptical, hyperbolic or parabolic cylinders with subsequent gluing of the formed edges. The obtained dislocations have an important property: variables in the corresponding Hamilton–Jacobi equation for geodesics are completely separable resulting in the Liouville integrability of geodesic equations. In addition, variables in the Laplace equation also admit complete separation of variables. To our knowledge, elliptic, hyperbolic and parabolic dislocations are described for the first time. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Applied Physics is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1142/S0217979226500438
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      – Code: eng
        Text: English
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        PageCount: 21
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    Subjects:
      – SubjectFull: Dislocation structure
        Type: general
      – SubjectFull: Elastic solids
        Type: general
      – SubjectFull: Hamilton-Jacobi equations
        Type: general
      – SubjectFull: Dislocations in crystals
        Type: general
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      – TitleFull: Elliptical, hyperbolic and parabolic dislocations.
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              Text: 2/20/2026
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              Y: 2026
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            – TitleFull: International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Applied Physics
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