Group classification of quasilinear elliptic-type equations. II. Invariance under solvable Lie algebras

2011 ◽  
Vol 63 (2) ◽  
pp. 236-253 ◽  
Author(s):  
V. I. Lahno ◽  
S. V. Spichak
Keyword(s):  
Lie Algebras ◽  
Group Classification ◽  
Elliptic Type ◽  
Solvable Lie Algebras ◽  
Quasilinear Elliptic

scholarly journals Classification of Symmetry Lie Algebras of the Canonical Geodesic Equations of Five-Dimensional Solvable Lie Algebras

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1354 ◽  
Author(s):  
Hassan Almusawa ◽  
Ryad Ghanam ◽  
Gerard Thompson
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Vector Fields ◽  
Solvable Lie Groups ◽  
Related System ◽  
Geodesic Equations ◽  
Solvable Lie Algebras ◽  
Symmetry Algebras

In this investigation, we present symmetry algebras of the canonical geodesic equations of the indecomposable solvable Lie groups of dimension five, confined to algebras A 5 , 7 a b c to A 18 a . For each algebra, the related system of geodesics is provided. Moreover, a basis for the associated Lie algebra of the symmetry vector fields, as well as the corresponding nonzero brackets, are constructed and categorized.

Group classification of third order nonlinear wave equations chain’s

2020 ◽  
Vol 15 (3-4) ◽  
pp. 232-237
Author(s):  
O.K. Babkov ◽  
G.Z. Mukhametova
Keyword(s):  
Lie Algebras ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Group Analysis ◽  
Group Classification ◽  
Nonlinear Wave Equations ◽  
Bäcklund Transformations ◽  
Third Order ◽  
A Chain

The paper presents the results of point symmetrys Lie algebras for third-order nonlinear wave equations calculating linked into a chain by Bäcklund transformations. Calculations are carried out by using Lie-Ovsyannikov method of group analysis. The basic algebras of point symmetries of the indicated equations are found, all possible cases of their extension are revealed, and the commutator tables of algebras found are calculated.

Classification and Isomorphisms of Non-degenerate Solvable Lie Algebras of Maximal Rank

2008 ◽  
Vol 15 (02) ◽  
pp. 347-360 ◽  
Author(s):  
Haishan Zhang ◽  
Caihui Lu
Keyword(s):  
Lie Algebras ◽  
Maximal Rank ◽  
Nilpotent Lie Algebras ◽  
Solvable Lie Algebras

The classification of nilpotent Lie algebras of maximal rank was solved by Santharoubane. In the present paper, we prove that the classification of non-degenerate solvable Lie algebras of maximal rank can be obtained from the work of Santharoubane.

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