This article is cited in 11 papers

Systems of linear differential equations symmetric with respect to transformations nonlinear in a function

Yu. A. Chirkunov

Novosibirsk State University for Economics and Management, Novosibirsk

Abstract: We show that if a system of first order linear differential equations with constant coefficients admits an operator whose coordinates responsible for the transformation of independent variables depend on functions then it admits an operator whose coordinates responsible for the transformation of functions depend nonlinearly on functions.

Keywords: system of first order linear differential equations with constant coefficients, equivalence transform, $\mathbf x$-autonomous operator, $\mathbf u$-nonlinear operator, $(\mathbf r,\mathbf l)$-pair, exclusive system, canonical system.

UDC: 517.944+519.46

Received: 15.11.2008

 English version: Siberian Mathematical Journal, 2009, 50:3, 541–546

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