2N-Dimensional Canonical Systems and Applications

TL;DR

This paper explores 2N-dimensional canonical systems, analyzing their fundamental solutions, Floquet theory, and asymptotic behavior, with applications in physics such as stability analysis, effective mass, water waves, and Dirac systems.

Contribution

It introduces new insights into the properties and Floquet theory of 2N-dimensional canonical systems and discusses their diverse physical applications.

Findings

Analysis of fundamental solutions of 2N-dimensional systems

Development of Floquet theory for periodic systems

Identification of applications in physics like stability and wave phenomena

Abstract

We study the 2N-dimensional canonical systems and discuss some properties of its fundamental solution. We then discuss the Floquet theory of periodic canonical systems and observe the asymptotic behavior of its solution. Some important physical applications of the systems are also discussed: linear stability of periodic Hamiltonian systems, position-dependent effective mass, pseudo-periodic nonlinear water waves, and Dirac systems.