Rational Constants of Generic LV Derivations and of Monomial Derivations

Volume 61 / 2013

Janusz Zieliński Bulletin Polish Acad. Sci. Math. 61 (2013), 201-208 MSC: Primary 13N15; Secondary 12H05, 92D25, 34A34. DOI: 10.4064/ba61-3-2


We describe the fields of rational constants of generic four-variable Lotka–Volterra derivations. Thus, we determine all rational first integrals of the corresponding systems of differential equations. Such systems play a role in population biology, laser physics and plasma physics. They are also an important part of derivation theory, since they are factorizable derivations. Moreover, we determine the fields of rational constants of a class of monomial derivations.


  • Janusz ZielińskiFaculty of Mathematics and Computer Science
    Nicolas Copernicus University
    Chopina 12/18
    87-100 Toruń, Poland

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