Nonlinear separable equations in linear spaces and commutative Leibniz algebras

D. Przeworska-Rolewicz. "Nonlinear separable equations in linear spaces and commutative Leibniz algebras." Annales Polonici Mathematici 97.3 (2010): 219-241. <http://eudml.org/doc/280372>.

@article{D2010,
abstract = {We consider nonlinear equations in linear spaces and algebras which can be solved by a "separation of variables" obtained due to Algebraic Analysis. It is shown that the structures of linear spaces and commutative algebras (even if they are Leibniz algebras) are not rich enough for our purposes. Therefore, in order to generalize the method used for separable ordinary differential equations, we have to assume that in algebras under consideration there exist logarithmic mappings. Section 1 contains some basic notions and results of Algebraic Analysis. In Section 2 we consider equations in linear spaces. Section 3 contains results for commutative Leibniz algebras. In Section 4 basic notions and facts concerning logarithmic and antilogarithmic mappings are collected. Section 5 is devoted to separable nonlinear equations in commutative Leibniz algebras with logarithms.},
author = {D. Przeworska-Rolewicz},
journal = {Annales Polonici Mathematici},
language = {eng},
number = {3},
pages = {219-241},
title = {Nonlinear separable equations in linear spaces and commutative Leibniz algebras},
url = {http://eudml.org/doc/280372},
volume = {97},
year = {2010},
}

TY - JOUR
AU - D. Przeworska-Rolewicz
TI - Nonlinear separable equations in linear spaces and commutative Leibniz algebras
JO - Annales Polonici Mathematici
PY - 2010
VL - 97
IS - 3
SP - 219
EP - 241
AB - We consider nonlinear equations in linear spaces and algebras which can be solved by a "separation of variables" obtained due to Algebraic Analysis. It is shown that the structures of linear spaces and commutative algebras (even if they are Leibniz algebras) are not rich enough for our purposes. Therefore, in order to generalize the method used for separable ordinary differential equations, we have to assume that in algebras under consideration there exist logarithmic mappings. Section 1 contains some basic notions and results of Algebraic Analysis. In Section 2 we consider equations in linear spaces. Section 3 contains results for commutative Leibniz algebras. In Section 4 basic notions and facts concerning logarithmic and antilogarithmic mappings are collected. Section 5 is devoted to separable nonlinear equations in commutative Leibniz algebras with logarithms.
LA - eng
UR - http://eudml.org/doc/280372
ER -