FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 3, PAGES 705-720

Integrable cubic ODEs on free associative algebras

O. V. Efimovskaya

Abstract

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ODEs with respect to two unknown functions belonging to the free associative algebra are considered. A complete classification of such equations possessing linear first integrals and at least one cubic infinitesimal symmetry is performed. Equations of arbitrary degree such that a trace of any polynomial is a first integral are investigated.

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Last modified: February 17, 2003