## Rational Constants of Generic LV Derivations and of Monomial Derivations

### Volume 61 / 2013

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

#### Abstract

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.