Abstract:
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, jet space.
Citation:
G. Manno, F. Oliveri, R. Vitolo, “Differential equations uniquely determined by algebras of point symmetries”, TMF, 151:3 (2007), 486–494; Theoret. and Math. Phys., 151:3 (2007), 843–850
This publication is cited in the following 13 articles:
Oliveri F., “Relie: a Reduce Program For Lie Group Analysis of Differential Equations”, Symmetry-Basel, 13:10 (2021), 1826
Gorgone M., Oliveri F., “Consistent Approximate Q-Conditional Symmetries of Pdes: Application to a Hyperbolic Reaction-Diffusion-Convection Equation”, Z. Angew. Math. Phys., 72:3 (2021), 119
Gorgone M., Oliveri F., “Lie Remarkable Partial Differential Equations Characterized By Lie Algebras of Point Symmetries”, J. Geom. Phys., 144 (2019), 314–323
Gorgone M., Oliveri F., “Nonlinear first order PDEs reducible to autonomous form polynomially homogeneous in the derivatives”, J. Geom. Phys., 113 (2017), 53–64
Pucci E., Saccomandi G., Vitolo R., “Bogus Transformations in Mechanics of Continua”, Int. J. Eng. Sci., 99 (2016), 13–21
Sergyeyev A., Vitolo R., “Symmetries and conservation laws for the Karczewska–Rozmej–Rutkowski–Infeld equation”, Nonlinear Anal.-Real World Appl., 32 (2016), 1–9
De Matteis G., Manno G., “Lie Algebra Symmetry Analysis of the Helfrich and Willmore Surface Shape Equations”, Commun. Pure Appl. Anal, 13:1 (2014), 453–481
Manno G., Oliveri F., Saccomandi G., Vitolo R., “Ordinary Differential Equations Described By Their Lie Symmetry Algebra”, J. Geom. Phys., 85 (2014), 2–15
White H., “Nonlocal symmetries and complete symmetry groups of dynamical systems admitting linearizations”, Nuovo Cimento Della Societa Italiana Di Fisica B-Basic Topics in Physics, 125:11 (2010), 1363–1378
Francesco Oliveri, “Lie Symmetries of Differential Equations: Classical Results and Recent Contributions”, Symmetry, 2:2 (2010), 658
Andriopoulos K., Dimas S., Leach P.G.L., Tsoubelis D., “On the systematic approach to the classification of differential equations by group theoretical methods”, J. Comput. Appl. Math., 230:1 (2009), 224–232
Myeni S.M., Leach P.G.L., “Complete symmetry group and nonlocal symmetries for some two-dimensional evolution equations”, J. Math. Anal. Appl., 357:1 (2009), 225–231
Dimas S., Andriopoulos K., Tsoubelis D., Leach P.G.L., “Complete specification of some partial differential equations that arise in financial mathematics”, Journal of Nonlinear Mathematical Physics, 16, Suppl. 1 (2009), 73–92