Geodesic
Differential equations uniquely determined by algebras of point symmetries
Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 3, pp. 486-494 Cet article a éte moissonné depuis la source Math-Net.Ru

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We continue to investigate strongly and weakly Lie remarkable equations, which we defined in a recent paper. We consider some relevant algebras of vector fields on $\mathbb{R}^k$ (such as the isometric, affine, projective, or conformal algebras) and characterize strongly Lie remarkable equations admitted by the considered Lie algebras.
Keywords: Lie symmetries of differential equations
Mots-clés : jet space. 
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G. Manno; F. Oliveri; R. Vitolo. Differential equations uniquely determined by algebras of point symmetries. Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 3, pp. 486-494. http://geodesic.mathdoc.fr/item/TMF_2007_151_3_a13/

[1] G. Baumann, Symmetry Analysis of Differential Equations with Mathematica, Springer, New York, 2000 ; G. W. Bluman, S. Kumei, Symmetries and Differential Equations, Appl. Math. Sci., 81, Springer, New York, 1989 ; N. H. Ibragimov, Transformation Groups Applied to Mathematical Physics, Math. Appl., 3, Reidel, Dordrecht–Boston–Lancaster, 1985 ; Handbook of Lie Group Analysis of Differential Equations, vols. I–III, ed. N. H. Ibragimov, CRC, Boca Raton, 1994, 1995, 1996 ; Л. В. Овсянников, Групповой анализ дифференциальных уравнений, М., Наука, 1978 | MR | Zbl | DOI | MR | Zbl | MR | Zbl | MR | MR | MR | Zbl | Zbl | Zbl | MR | MR | Zbl | Zbl

[2] G. W. Bluman, J. D. Cole, Similarity Methods of Differential Equations, Appl. Math. Sci., 13, Springer, New York, 1974 | DOI | MR | Zbl

[3] Cimmetrii i zakony sokhraneniya uravnenii matematicheskoi fiziki, eds. A. M. Vinogradov, I. S. Krasilschik, Faktorial, M., 1997 | MR | Zbl

[4] P. Olver, Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1989 | MR | MR | Zbl | Zbl

[5] P. J. Olver, Equivalence, Invariants, and Symmetry, Cambridge Univ. Press, New York, 1995 | MR | Zbl

[6] W. I. Fushchych, I. Yehorchenko, Acta Appl. Math., 28 (1992), 69–92 ; G. Rideau, P. Winternitz, J. Math. Phys., 31 (1990), 1095–1105 | MR | Zbl | DOI | MR | Zbl

[7] G. Manno, F. Oliveri, R. Vitolo, “On differential equations characterized by their Lie point symmetries”, J. Math. Anal. Appl., 332:2 (2007), 767–786 | DOI | MR | Zbl

[8] G. Manno, F. Oliveri, R. Vitolo, “On an inverse problem in group analysis of PDEs: Lie-remarkable equations”, Waves and Stability in Continuous Media, Proc. XIII Conf. (Catania, Italy, 2005), eds. R. Monaco, G. Mulone, S. Rionero, T. Ruggeri, World Sci. Publ., Hackensack, New York, 2006, 420–432 | MR

[9] F. Oliveri, Note Mat., 23:2 (2004/2005), 195–216 ; “Sur une propriété remarquable des équations de Monge-Ampère”, Non Linear Hyperbolic Fields and Waves. A tribute to Guy Boillat, Rend. Circ. Mat. Palermo (2) Suppl., no. 78, 2006, 243–257 | MR | Zbl | MR | Zbl

[10] V. Rosenhaus, On one-to-one correspondence between the equation and its group. The Monge–Ampère equation, Preprint F. 18, Acad. Sci. Estonian SSR, Tartu, 1982; Algebras Groups Geom., 3 (1986), 148–166 ; 5 (1988), 137–150 | MR | Zbl | MR | Zbl

[11] G. Boillat, C. R. Acad. Sci. Paris, 313 (1991), 805–808 | MR | Zbl

[12] D. J. Saunders, The Geometry of Jet Bundles, London Math. Soc. Lect. Note Ser., 142, Cambridge Univ. Press, Cambridge, 1989 | MR | Zbl

[13] W. I. Fushchych, Scientific Works, v. 2 (1979–1985), ed. V. Boyko, Kyiv, 2000 ; http://www.imath.kiev.ua/f̃ushchych/papers/Volume2.pdf | Zbl

[14] G. Boillat, C. R. Acad. Sci. Paris, 315 (1992), 1211–1214 | MR | Zbl