The Method of an Exact Linearization of n-order Ordinary Differential Equations

DOI

10.2991/jnmp.1996.3.3-4.12How to use a DOI?

Abstract

Necessary and sufficient conditions are found that the n-order nonlinear and nonautonomous ordinary differential equation could be transformed into a linear equation with constant coefficients with the help, generally speaking, nonlocal transformation of dependent and independent variables. These conditions are expressed in termes of factorization through first order nonlinear differential operators. Examples are considered also. "Two subjects that are theoretical physics and integration of differential equations, are quitely impossible one without another, were always developing together, and the success of one of them influenced another" (V.P. Ermakov)

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - L.M. Berkovich
PY  - 1996
DA  - 1996/09/02
TI  - The Method of an Exact Linearization of n-order Ordinary Differential Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 341
EP  - 350
VL  - 3
IS  - 3-4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1996.3.3-4.12
DO  - 10.2991/jnmp.1996.3.3-4.12
ID  - Berkovich1996
ER  -