Janusz Zielinski
Abstract:
We describe all rational constants of a large family of four-variable
cyclic factorizable derivations. Thus, we determine all rational
first integrals of their corresponding systems of differential equations.
Moreover, we give a characteristic of all four-variable Lotka-Volterra
derivations with a nontrivial rational constant.
All considerations are over an arbitrary field of characteristic zero.
Our main tool is the investigation of the cofactors of strict Darboux
polynomials. Factorizable derivations are important in derivation theory.
Namely, we may associate the factorizable derivation with any given
derivation of a polynomial ring and that construction
helps to determine rational constants of arbitrary derivations.
Besides, Lotka-Volterra systems play a significant role in population
biology, laser physics and plasma physics.
Submitted November 12, 2014. Published December 21, 2015.
Math Subject Classifications: 34A34, 13N15, 12H05, 92D25.
Key Words: Lotka-Volterra derivation; factorizable derivation;
rational constant; rational first integral.
Show me the PDF file (195 KB), TEX file, and other files for this article.
Janusz Zielinski Faculty of Mathematics and Computer Science N. Copernicus University, ul. Chopina 12/18 87-100 Torun, Poland email: ubukrool@mat.uni.torun.pl |
Return to the EJDE web page