This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy functional. Contrary to the Laplacian appearing in the equations of nonrelativistic quantum mechanics, the Dirac operator has a negative continuous spectrum which is not bounded fr...

In this paper we use a transfer matrix method to calculate the asymptotic behavior of the nonlinear Schrödinger (NLS) equation in a self-defocusing medium for piecewise constant initial conditions. Treating initial conditions that consist of m repeated regions, we show that the eigenvalues associated with this problem appear in bands, and, as m tends to infinity, we obtain the eigenvalue densit...

In this paper, nonlinear rigid body dynamics for rotorcraft mathematical model is studied. A linearization of helicopter flight dynamics is evaluated. Automatic Flight Control System (AFCS) with gain scheduled LQ optimal control is designed based on look-up tables. Stability analyses are performed and results are illustrated graphically for open and closed-loop systems. As seen from results, LQ...