A modification of a classical method to obtain Floquet exponents and
solutions for linear periodic differential equations.
- Manuel Gadella,
- Luis Pedro Lara
Abstract
We propose a modification of a method based on Fourier analysis to
obtain the Floquet characteristic exponents for periodic homogeneous
linear systems, which shows a high precision. This modification uses a
variational principle to find the correct Floquet exponents among the
solutions of an algebraic equation. Once we have these Floquet
exponents, we determine explicit approximated solutions. We test our
results on systems for which exact solutions are known to verify the
accuracy of our method including one dimensional periodic potentials of
interest in quantum physics. Using the equivalent linear system, we also
study approximate solutions for homogeneous linear equations with
periodic coefficients.22 Sep 2022Submitted to Mathematical Methods in the Applied Sciences 23 Sep 2022Submission Checks Completed
23 Sep 2022Assigned to Editor
30 Sep 2022Reviewer(s) Assigned
24 Nov 2022Review(s) Completed, Editorial Evaluation Pending
25 Nov 2022Editorial Decision: Revise Major
20 Dec 20221st Revision Received
24 Dec 2022Submission Checks Completed
24 Dec 2022Assigned to Editor
24 Dec 2022Review(s) Completed, Editorial Evaluation Pending
24 Dec 2022Reviewer(s) Assigned
27 Dec 2022Editorial Decision: Accept