Multi-Hamiltonian property of a linear system with quadratic invariant

2019 ◽  
Vol 30 (5) ◽  
pp. 877-883 ◽  
Author(s):  
V. V. Kozlov
Keyword(s):  
Linear System ◽  
Quadratic Invariant ◽  
Hamiltonian Property

scholarly journals Linear System of Differential Equations with a Quadratic Invariant as the Schrödinger Equation

2021 ◽  
Author(s):  
V. V. Kozlov
Keyword(s):  
Linear System ◽  
Schrödinger Equation ◽  
Differential Equations ◽  
Schrodinger Equation ◽  
Real Hilbert Space ◽  
Complex Structure ◽  
Complete Orthonormal System ◽  
Basic Principles ◽  
Linear Partial Differential Equations ◽  
Quadratic Invariant

Abstract Linear systems of differential equations with an invariant in the form of a positive definite quadratic form in a real Hilbert space are considered. It is assumed that the system has a simple spectrum and the eigenvectors form a complete orthonormal system. Under these assumptions, the linear system can be represented in the form of the Schrödinger equation by introducing a suitable complex structure. As an example, we present such a representation for the Maxwell equations without currents. In view of these observations, the dynamics defined by some linear partial differential equations can be treated in terms of the basic principles and methods of quantum mechanics.

Chaos in a manifold piecewise linear system

1981 ◽  
Vol 64 (10) ◽  
pp. 9-17 ◽  
Author(s):  
Toshimichi Saito ◽  
Hiroichi Fujita
Keyword(s):  
Linear System ◽  
Piecewise Linear ◽  
Piecewise Linear System

Impossibility of steady squeezing for two-mode linear system without self-action

1991 ◽  
Vol 1 (9) ◽  
pp. 1217-1227 ◽  
Author(s):  
A. A. Bakasov ◽  
N. V. Bakasova ◽  
E. K. Bashkirov ◽  
V. Chmielowski
Keyword(s):  
Linear System
Sign in / Sign up

Export Citation Format

Share Document