One of the challenges of the modern photonics is to develop all-optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested ParityTime (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non-conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT-symmetric photonic systems with an intensitydependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly-induced PT-symmetry breaking, and all-optical switching. Nonlinear PT-symmetric systems can serve as powerful building blocks for the development of novel photonic devices targeting an active light control.

Dynamics of a chain of interacting parity-time-invariant nonlinear dimers is investigated. A dimer is built as a pair of coupled elements with equal gain and loss. A relation between stationary soliton solutions of the model and solitons of the discrete nonlinear Schrödinger (DNLS) equation is demonstrated. Approximate solutions for solitons whose width is large in comparison to the lattice spacing are derived, using a continuum counterpart of the discrete equations. These solitons are mobile, featuring nearly elastic collisions. Stationary solutions for narrow solitons, which are immobile due to the pinning by the effective Peierls-Nabarro potential, are constructed numerically, starting from the anticontinuum limit. The solitons with the amplitude exceeding a certain critical value suffer an instability leading to blowup, which is a specific feature of the nonlinear parity-time-symmetric chain, making it dynamically different from DNLS lattices. A qualitative explanation of this feature is proposed. The instability threshold drops with the increase of the gain-loss coefficient, but it does not depend on the lattice coupling constant, nor on the soliton's velocity.

We study nonlinear binary arrays composed of parity-time-symmetric optical waveguides with gain and loss. We demonstrate that such nonlinear binary lattices support stable discrete solitons, which can be adiabatically tuned and switched through nonlinear symmetry breaking by varying gain and loss parameters.

van der Waals heterostructures, obtained by stacking layers of isolated two-dimensional atomic crystals like graphene (GE) and silicene (SE), are one of emerging nanomaterials for the development of future multifunctional devices. Thermal transport behaviors at the interface of these heterostructures play a pivotal role in determining their thermal properties and functional performance. Using molecular dynamics simulations, the interfacial thermal conductance G of an SE/GE bilayer heterostructure is studied. Simulations show that G of a pristine SE/GE bilayer at room temperature is 11.74 MW/m(2)K when heat transfers from GE to SE, and is 9.52 MW/m(2)K for a reverse heat transfer, showing apparent thermal rectification effects. In addition, G increases monotonically with both the temperature and the interface coupling strength. Furthermore, hydrogenation of GE is efficient in enhancing G if an optimum hydrogenation pattern is adopted. By changing the hydrogen coverage f, G can be controllably manipulated and maximized up to five times larger than that of pristine SE/GE. This study is helpful for understanding the interface thermal transport behaviors of novel van der Waals heterostructures and provides guidance for the design and control of their thermal properties.

We consider a discrete two-dimensional model of a crystal with particles having rotational degrees of freedom. We derive the equations of motion and analyze its continuum analog obtained in the long-wave limit. The continuum equations are shown to be the ones of the micropolar elasticity theory. The conditions when the micropolar elasticity equations can be reduced to the equations of conventional elasticity theory are discussed. We show that the rotational degrees of freedom are responsible for the anomalies in the elastic properties of some of the dielectric crystals.

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We show that the parity-time (PT ) symmetric coupled optical waveguides with gain and loss support localised oscillatory structures similar to the breathers of the classical φ 4 model. The power carried by the PT -breather oscillates periodically, switching back and forth between the waveguides, so that the gain and loss are compensated on the average. The breathers are found to coexist with solitons and be prevalent in the products of the soliton collisions. We demonstrate that the evolution of the small-amplitude breather's envelope is governed by a system of two coupled nonlinear Schrödinger equations, and employ this Hamiltonian system to show that the smallamplitude PT -breathers are stable.

For the nonlinear Klein-Gordon type models, we describe a general method of discretization in which the static kink can be placed anywhere with respect to the lattice. These discrete models are therefore free of the static Peierls-Nabarro potential. Previously reported models of this type are shown to belong to a wider class of models derived by means of the proposed method. A relevant physical consequence of our findings is the existence of a wide class of discrete Klein-Gordon models where slow kinks practically do not experience the action of the Peierls-Nabarro potential. Such kinks are not trapped by the lattice and they can be accelerated by even weak external fields.