Related papers: 2N-Dimensional Canonical Systems and Applications

For a family of second-order parabolic systems with rapidly oscillating and time-dependent periodic coefficients, we investigate the asymptotic behavior of fundamental solutions and establish sharp estimates for the remainders.

For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…

Periodically driven systems have emerged as a useful technique to engineer the properties of quantum systems, and are in the process of being developed into a standard toolbox for quantum simulation. An outstanding challenge that leaves…

In this paper, we are interested in the two-dimensional Dirac-Klein-Gordon system, which is a basic model in particle physics. We investigate the global behaviors of small data solutions to this system in the case of a massive scalar field…

We study an analog of the classical Arnol'd diffusion in a quantum system of two coupled non-linear oscillators one of which is governed by an external periodic force with two frequencies. In the classical model this very weak diffusion…

In this paper, we analyse the long-time behavior of solutions to a coupled system describing the motion of a rigid disk in a 2D viscous incompressible fluid. Following previous approaches, we look at the problem in the system of coordinates…

The Darbroux transformation is generalized for time-dependent Hamiltonian systems which include a term linear in momentum and a time-dependent mass. The formalism for the $N$-fold application of the transformation is also established, and…

The invariance for the equation of fast diffusion in the 2D coordinate space has been proved, and its reduction to the 1D (with respect to the spatial variable) analog is demonstrated. On the basis of these results, new exact…

We develop a numerical method based on canonical conformal variables to study two eigenvalue problems for operators fundamental to finding a Stokes wave and its stability in a 2D ideal fluid with a free surface in infinite depth. We…

Based on continuity properties of the de Branges correspondence, we develop a new approach to study the high-energy behavior of Weyl-Titchmarsh and spectral functions of $2\times2$ first order canonical systems. Our results improve several…

We introduce notions of vector field and its (discrete time) flow on a chain complex. The resulting dynamical systems theory provides a set of tools with a broad range of applicability that allow, among others, to replace in a canonical way…

We study models kinetic models of polymeric fluids. We introduce a notion of solutions which is based on moments of polymeric distributions. We prove global existence and uniqueness of a large class of initial data for diffusive systems of…

This paper describes the Floquet theory for quaternion-valued differential equations (QDEs). The Floquet normal form of fundamental matrix for linear QDEs with periodic coefficients is presented and the stability of quaternionic periodic…

In this work we present an analogue of the inverse scattering for Canonical systems using theory of vessels and associated to them completely integrable systems. Analytic coefficients fits into this setting, significantly expanding the…

This paper provides two results that are useful in the study of the existence and the stability properties of a periodic solution for a given dynamical system. The first result deals with scalar time-periodic systems and establishes the…

In this paper, we investigate the existence and the global stability of periodic solution for dynamical systems with periodic interconnections, inputs and self-inhibitions. The model is very general, the conditions are quite weak and the…

The dynamics of five-dimensional Chern-Simons theories is analyzed. These theories are characterized by intricate self couplings which give rise to dynamical features not present in standard theories. As a consequence, Dirac's canonical…

The Dirac method treatment for finite dimensional singular systems with weakly vanishing Hamiltonian leads to obtain the equations of motion in terms of parameter $\tau$. To obtain the correct equations of motion one should use gauge fixing…

In this paper we study global existence of weak solutions for the Quantum Hydrodynamics System in 2-D in the space of energy. We do not require any additional regularity and/or smallness assumptions on the initial data. Our approach…

In the paper a two-dimensional integro-differential system is considered. Using some variational methods we give sufficient conditions for the existence and uniqueness of a solution to the considered system. Moreover, we show that the…