A. B. Shabat, M. Kh. Efendiev, “On applications of Faà-di-Bruno formula”, Ufimsk. Mat. Zh., 2017, Volume 9, Issue 3,Pages <nobr>132

This article is cited in 3 papers

On applications of Faà-di-Bruno formula

A. B. Shabat^abc, M. Kh. Efendiev^b

^a Institute of Mathematics, Ufa Scientific Center, RAS, Chernyshevsky str. 112, 450077, Ufa, Russia
^b Karachay-Circassian State University named after U.D. Aliev, Lenin str. 23, 369200, Karachaevsk, Russia
^c L.D. Landau Institute for Theoretical Physics, RAS, Academician Semenov av. 1-A, 142432, Chernogolovka, Russia

Abstract: In the work we construct two modifications of the classical Faà-di-Bruno formula. We consider the applications of these formulae in the integrability theory for nonlinear partial differential equations. We discuss the problem on integration by parts in the Gelfand–Olver–Sanders formal variational calculus.

Keywords: Faà-di-Bruno formula, differential polynomials, integrability conditions.

UDC: 512.5

MSC: 37K10

Received: 08.04.2017