Raisa Khamitova

Utilization of Photon Orbital Angular Momentum in the Low-Frequency Radio Domain

We show numerically that vector antenna arrays can generate radio beams that exhibit spin and orbital angular momentum characteristics similar to those of helical Laguerre-Gauss laser beams in paraxial optics. For low frequencies (< or = 1 GHz), digital techniques can be used to coherently measure the instantaneous, local field vectors and to manipulate them in software. This enables new types of experiments that go beyond what is possible in optics. It allows information-rich radio astronomy and paves the way for novel wireless communication concepts.

Self-adjointness of a generalized Camassa–Holm equation

Abstract It is well known that the Camassa–Holm equation possesses numerous remarkable properties characteristic for KdV type equations. In this paper we show that it shares one more property with the KdV equation. Namely, it is shown in [1] , [2] that the KdV and the modified KdV equations are self-adjoint. Starting from the generalization [3] of the Camassa–Holm equation [4] , we prove that the Camassa–Holm equation is self-adjoint. This property is important, e.g. for constructing conservation laws associated with symmetries of the equation in question. Accordingly, we construct conservation laws for the generalized Camassa–Holm equation using its symmetries.

Conservation laws for the Maxwell-Dirac equations with dual Ohm’s law

Using a general theorem on conservation laws for arbitrary differential equations proved by Ibragimov [J. Math. Anal. Appl. 333, 311–320 (2007)], we have derived conservation laws for Dirac’s symmetrized Maxwell-Lorentz equations under the assumption that both the electric and magnetic charges obey linear conductivity laws (dual Ohm’s law). We find that this linear system allows for conservation laws which are nonlocal in time.

Conservation Laws in Thomas’s Model of Ion Exchange in a Heterogeneous Solution

Physically significant question on calculation of conservation laws of the Thomas equation is investigated. It is demonstrated that the Thomas equation is nonlinearly self-adjoint. Using this property and applying the theorem on nonlocal conservation laws the infinite set of conservation laws corresponding to the symmetries of the Thomas equation is computed. It is shown that the Noether theorem provide only one of these conservation laws.