A variational modification of the Harmonic Balance method to obtain approximate Floquet exponents

Abstract

We propose a modification of a method based on Fourier analysis to obtainthe Floquet characteristic exponents for periodic homogeneous linear systems,which shows a high precision. This modification uses a variational principle tofind the correct Floquet exponents among the solutions of an algebraic equation.Once we have these Floquet exponents, we determine explicit approximatedsolutions. We test our results on systems for which exact solutions are knownto verify the accuracy of our method including one-dimensional periodicpotentials of interest in quantum physics. Using the equivalent linear system,we also study approximate solutions for homogeneous linear equations withperiodic coefficients.