Continuous changes of variables and the Magnus expansion
arXiv:1907.05362 · doi:10.1088/2399-6528/ab42c1
Abstract
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 Schrödinger equation on the torus.
19 pages, 2 figures