In this paper energy bands and Berry curvature of graphene was studied. Desired Hamiltonian regarding the next-nearest neighbors obtained by tight binding model. By using the second quantization approach, the transformation matrix is calculated and the Hamiltonian of system is diagonalized. With this Hamiltonian, the band structure and wave function can be calculated. By using calculated wave f...

Hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers. However solutions which look like moving discrete breathers for some time are not difficult to observe in numerics. In this paper we propose an abstract framework for the description of approximate travelling discrete breathers in Hamiltonian chains of oscillators. The method is based on th...

The direct discrete time control of Port Controlled Hamiltonian Systems (PCHS) in the sense of energy shaping and damping injection is considered. In order to give a direct discrete time design method for PCHS, firstly an appropriate discrete gradient is proposed, which enables the derivation of a discrete time equation corresponding to the discrete time counterpart of Hamiltonian Systems. Usin...

In this article we prove that the discrete eigenvalues of the Zakharov-Shabat system belong to certain neighborhoods of the endpoints of the spectral gap and the discrete eigenvalue of the free Hamiltonian.

In this paper we consider the relation between symmetries and first integrals for both continuous canonical Hamiltonian equations and discrete Hamiltonian equations. We observe that canonical Hamiltonian equations can be obtained by variational principle from an action functional and consider invariance properties of this functional as it is done in Lagrangian formalism. We rewrite the well–kno...

Structural stability and the persistence of coherent structures under perturbations of a dynamical system are fundamental issues in dynamical systems theory with implications in many fields of application. In the context of discrete, finite dimensional Hamiltonian systems, this issue is addressed by the celebrated KAM theorem, which guarantees the persistence of most invariant tori of the unper...

‎In this paper Lie point symmetries‎, ‎Hamiltonian equations and conservation‎ ‎laws of general three-dimensional anisotropic non-linear sourceless heat transfer‎ ‎equation are investigated‎. ‎First of all Lie symmetries are obtained by using the general method‎ based on invariance condition of a system of differential equations under a pro‎longed vector field‎. ‎Then the structure of symmetry ...