TY - GEN

T1 - On the integration of a class of nonlinear systems of ordinary differential equations

AU - Talyshev, Aleksandr A.

PY - 2017/11/14

Y1 - 2017/11/14

N2 - For each associative, commutative, and unitary algebra over the field of real or complex numbers and an integrable nonlinear ordinary differential equation we can to construct integrable systems of ordinary differential equations and integrable systems of partial differential equations. In this paper we consider in some sense the inverse problem. Determine the conditions under which a given system of ordinary differential equations can be represented as a differential equation in some associative, commutative and unitary algebra. It is also shown that associativity is not a necessary condition.

AB - For each associative, commutative, and unitary algebra over the field of real or complex numbers and an integrable nonlinear ordinary differential equation we can to construct integrable systems of ordinary differential equations and integrable systems of partial differential equations. In this paper we consider in some sense the inverse problem. Determine the conditions under which a given system of ordinary differential equations can be represented as a differential equation in some associative, commutative and unitary algebra. It is also shown that associativity is not a necessary condition.

UR - http://www.scopus.com/inward/record.url?scp=85036582751&partnerID=8YFLogxK

U2 - 10.1063/1.5012679

DO - 10.1063/1.5012679

M3 - Conference contribution

AN - SCOPUS:85036582751

VL - 1907

T3 - AIP Conference Proceedings

BT - Proceedings of the 8th International Conference on Mathematical Modeling, ICMM 2017

A2 - Egorov, IE

A2 - Popov, SV

A2 - Vabishchevich, PN

A2 - Antonov, MY

A2 - Lazarev, NP

A2 - Troeva, MS

A2 - Troeva, MS

A2 - Ivanova, AO

A2 - Grigorev, YM

PB - American Institute of Physics Inc.

T2 - 8th International Conference on Mathematical Modeling, ICMM 2017

Y2 - 4 July 2017 through 8 July 2017

ER -