  In this paper, we are concerned with a formulation of Magnus and
Floquet-Magnus expansions for general nonlinear differential equations. To this
aim, we introduce suitable continuous variable transformations generated by
operators. As an application of the simple formulas so-obtained, we explicitly
compute the first terms of the Floquet-Magnus expansion for the Van der Pol
oscillator and the nonlinear Schr\"odinger equation on the torus.
