On applications of Faà-di-Bruno formula

Authors

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

DOI:

https://doi.org/10.13108/2017-9-3-131

Keywords:

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

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.

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Published

20.09.2017

Issue

Vol. 9 No. 3 (2017): Ufa Mathematical Journal 2017, volume 9 , issue 3

Section

Article