Current status. At the present time the nonlinear resonance waves of SIT in 2D (graphene) monolayer have been considered by Adamashvili [2014, 2015] only for SPPs and waveguide modes. But the nonlinear resonance and blended optical and acoustic waves (solitons, breathers, vector solitons) of SIT in 2D nanostructure, anisotropic semiconductor QDs and bi-anisotropic NIM have not been considered. It should be emphasized that those phenomena have not yet been modeled within the Finite Diffrenece Time Domain (FDTD) method. The solitonic mechanism of magneto-acoustic resonance in 2D antiferromagnets and the spin-quadrupole solitons in high-spin 2D ferromagnetics in presence of the acoustic and optical branches of excitations are unexplored.

Expected results and perspectives. An adequate theory of the SIT in 2D nanostructures, anisotropic semiconductor QDs, 2D magnetics and bi-anisotropic NIM under strong nonequilibrium conditions and dissipation will be constructed. After the implementation of this project,, it will be possible to obtain more complete and detail physical picture of the processes of formation, propagation, stability and evolution of the parameters of the of 2? - and 0? - pulses of SIT in these nanostructures. Explicit analytic expressions together with FDTD simulations will be developed for the parameters of nonlinear SPPs both in conservative as well as in dissipative physical systems of the 2D nanostructures, anisotropic semiconductor QDs and bi-anisotropic NIM in the presence the optical conductivity and strong optical nonlinearity of graphene. The parameters of dissipative optical solitons under strong nonequilibrium conditions and dissipation, to study the transition between the ballistic and dissipative limit, will be obtained. The conditions of instability of the nonlinear waves in 2D nanostructures will be determined. These outcomes are important and will contribute significantly to our understanding of the properties of resonance nonlinear waves in 2D materials, QDs and NIM. A comparison of the new theoretical results with the experiments will allow us to understand better the most interesting directions of the future development of the theory of SIT, in particular, and of the nonlinear waves theory generally. The properties of the wave processes near the point where a refractive index changes its sign will be considered, for the propagation of electromagnetic waves in bi-anisotropic (chiral) negative to positive transition metamaterials with a two-dimensional sheet of anisotropic semiconductor QDs and graphene monolayer. Explicit analytic expressions for the parameters of dissipative surface acoustic solitons in graphene under strong nonequilibrium conditions and dissipation, to study the transition between the dissipative and ballistic limit, will be obtained. The topological and breather-like solitons in 2D magnetics with single-ion anisotropy coupled with acoustic wave will be studied. The interaction of topological and dynamical solitons in 2D magnetics will be investigated. Numerical simulation of behavior of particle-like excitations under external pumping and dissipation in 2D magnetics will be presented.

Scope of activities. The following activities will be implemented under the Project: optical resonance solitons of SIT of the SPPs in 2D nanostructures; optical blended breathers of SPPs in 2D materials; optical resonance vector soliton with the sum and difference of the frequencies of SPPs in 2D nanostructures;optical non-resonance vector solitons with the sum and difference of the frequencies of SPPs in 2D nanostructures; optical dissipative solitons of SPPs in 2D nanostructures; the electromagnetic waves in bi-anisotropic (chiral) negative to positive transition metamaterials with a two-dimensional sheet of anisotropic semiconductor QDs and monolayer graphene; acoustic surface solitons in QDs and 2D nanostructures; simulation of nonlinear wave equations in 2D nanostructures using FDTD codes.; tunneling in magnetic nanostructures; magnetic and magneto-acoustic solitons and breathers in 2D materials; the interaction of topological and dynamical solitons; dynamical and topological solitons in single-ion 2D ferromagnet; numerical simulation of behavior of particle-like excitations under external pumping and dissipation; almost soliton and periodic soliton waves for the 2D KDV type of equations; analytical and numerical solution of 2D Burgesrs type of equation.