On geometry of solutions to approximate equations and their symmetries
Ufa mathematical journal, Tome 9 (2017) no. 2, pp. 40-54
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The paper is devoted to developing a geometric approach to the theory of approximate equations (including ODEs and PDEs) and their symmetries. We introduce dual Lie algebras, manifolds over dual numbers and dual Lie group. We describe some constructions applied for these objects. On the basis of these constructions, we show how one can formulate basic concepts and methods in the theory of approximate equations and their symmetries. The proofs of many general results here can be obtained almost immediately from classical ones, unlike the methods used for studying the approximate equations.
Keywords:
approximate equation, approximate Lie algebra, dual numbers, dual Lie algebra, manifold over dual numbers.
@article{UFA_2017_9_2_a3,
author = {V. V. Gorbatsevich},
title = {On geometry of solutions to approximate equations and their symmetries},
journal = {Ufa mathematical journal},
pages = {40--54},
publisher = {mathdoc},
volume = {9},
number = {2},
year = {2017},
language = {en},
url = {http://geodesic.mathdoc.fr/item/UFA_2017_9_2_a3/}
}
V. V. Gorbatsevich. On geometry of solutions to approximate equations and their symmetries. Ufa mathematical journal, Tome 9 (2017) no. 2, pp. 40-54. http://geodesic.mathdoc.fr/item/UFA_2017_9_2_a3/