Some theory and applications of 2N-dimensional canonical systems: periodic and nonperiodic

Abstract

Abstract In this paper, we study the 2N-dimensional canonical systems and their physical applications. We first discuss some basic theory including proving the existence of solutions of any canonical system and establish some properties of its fundamental solution. Then we discuss the periodic canonical systems, establish Floquet theory, and observe the asymptotic behavior of their solutions. We also explore some important physical applications of the systems, namely linear stability of periodic Hamiltonian systems, position-dependent effective mass, and pseudo-periodic nonlinear water waves.