Asymptotic decomposition of completely integrable Pfaffian systems with small parameter
type: Item
instance of: scholarly article
title: Asymptotic decomposition of completely integrable Pfaffian systems with small parameter
zbMATH Open document ID: 0701.34053
DOI: 10.1007/BF01061309
published in: Ukrainian Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: The method of asymptotic decomposition is extended to systems of the form \((1)\quad dx=(\Omega (x)+\epsilon {\tilde \Omega}(\epsilon,x))dt,\) \(x(t_ 0)=x_ 0\) where x is an n-dimensional vector and t is an m- dimensional vector. The system (1) is considered completely integrable. The authors introduce transformations which map the system (1) onto the differential system for slow variables and a differential system for fast variables. The system for slow variables can be solved separately and the system for fast variables can be then solved by quadratures. Further, the properties of the corresponding operators are analyzed.
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 4148599
zbMATH Keywords: completely integrable system
zbMATH Keywords: small parameter
zbMATH Keywords: method of asymptotic decomposition
author: Yu. A. Mitropol'skij
author: Alexey K. Lopatin
MaRDI profile type: Publication
cites work: Asymptotic decomposition of differential systems with a small parameter
full work available at URL: https://doi.org/10.1007/bf01061309
OpenAlex ID: W2039086604
description: scientific article; zbMATH DE number 4148599