Continuous changes of variables and the Magnus expansion

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.

arXiv comment19 pages, 2 figures

References in corpus (5)

• The Magnus expansion and some of its applications
• Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems
• Sufficient conditions for the convergence of the Magnus expansion
• Convergence of the Magnus series
• A Magnus- and Fer-type formula in dendriform algebras