RELATIVISTIC PARTICLES ALONG NULL CURVES IN 3D LORENTZIAN SPACE FORMS
2010 ◽
Vol 20
(09)
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pp. 2851-2859
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Keyword(s):
We study relativistic particles modeled by actions whose Lagrangians are arbitrary functions on the curvature of null paths in (2 + 1)-dimensions backgrounds with constant curvature. We obtain first integrals of the Euler–Lagrange equation by using geometrical methods involving the search for Killing vector fields along critical curves of the action. In the case in which Lagrangian density depends quadratically on Cartan curvature, it is shown that the mechanical system is governed by a stationary Korteweg–De Vries system. Motion equations are completely integrated by quadratures in terms of elliptic and hyperelliptic functions.
2015 ◽
Vol 12
(10)
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pp. 1550111
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Keyword(s):
2001 ◽
Vol 16
(30)
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pp. 4845-4863
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Keyword(s):
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2012 ◽
Vol 10
(2)
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pp. 1051-1065
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Keyword(s):
2010 ◽
Vol 81
(3)
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pp. 496-506
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Keyword(s):
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2020 ◽
Vol 0
(0)
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Keyword(s):