Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

Dispersive, superfluid-like shock waves in nonlinear optics

In most classical fluids, shock waves are strongly dissipative, their energy being quickly lost through viscous damping. But in systems such as cold plasmas, superfluids, and Bose-Einstein condensates, where viscosity is negligible or non-existent, a fundamentally different type of shock wave can emerge whose behaviour is dominated by dispersion rather than dissipation. Dispersive shock waves are difficult to study experimentally, and analytical solutions to the equations that govern them have only been found in one dimension (1D). By exploiting a well-known, but little appreciated, correspondence between the behaviour of superfluids and nonlinear optical materials, we demonstrate an all-optical experimental platform for studying the dynamics of dispersive shock waves. This enables us to observe the propagation and nonlinear response of dispersive shock waves, including the interaction of colliding shock waves, in 1D and 2D. Our system offers a versatile and more accessible means for exploring superfluid-like and related dispersive phenomena.Comment: 21 pages, 6 figures Revised abstrac

Nonlinearity and Topology

The interplay of nonlinearity and topology results in many novel and emergent properties across a number of physical systems such as chiral magnets, nematic liquid crystals, Bose-Einstein condensates, photonics, high energy physics, etc. It also results in a wide variety of topological defects such as solitons, vortices, skyrmions, merons, hopfions, monopoles to name just a few. Interaction among and collision of these nontrivial defects itself is a topic of great interest. Curvature and underlying geometry also affect the shape, interaction and behavior of these defects. Such properties can be studied using techniques such as, e.g. the Bogomolnyi decomposition. Some applications of this interplay, e.g. in nonreciprocal photonics as well as topological materials such as Dirac and Weyl semimetals, are also elucidated

Distribution and phylogeny of Hyalomma ticks (Acari: Ixodidae) in Turkey

The genus Hyalomma includes some of the most medically and veterinarily important tick species in the world. To clarify and identify the current distribution of the species of Hyalomma, field studies were conducted in 65 localities in Turkey and five localities in Cyprus. Additionally, using mitochondrial 12S and 16S ribosomal DNA, specimens of Hyalomma from Turkey, H. excavatum from Cyprus, H. marginatum from Spain and Italy were evaluated together with the available sequences obtained from Genbank. Morphological and molecular analyses demonstrated the presence of four species in Turkey: H. marginatum, H. excavatum, H. aegyptium and H. asiaticum. Hyalomma marginatum is the dominant species in the Central and Northern parts of Turkey, whereas H. excavatum distributes mostly in the Southern parts. Hyalomma asiaticum is restricted to the Southeastern Anatolia. However, some sympatric regions were observed for these species. Phylogenetic trees obtained with Maximum Likelihood method demonstrated five clades. Data supported previous conclusions, but placed H. asiaticum, H. scupense, H. dromedarii and H. aegyptium in different clades with high bootstrap values. Specimens of H. anatolicum group and H. marginatum complex are sister groups. Pairwise distance analyses of these groups showed 2.8 and 3% differences for 12S rDNA and 16S rDNA, respectively. Therefore, additional analyses with the samples from different locations using different markers need to evaluate the exact status of the species of these groups