9,637 research outputs found

    Bäcklund transformations, energy shift and the plane wave limit

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    We discuss basic properties of the Bäcklund transformations for the classical string in AdS space in the context of the null-surface perturbation theory. We explain the relation between the Bäcklund transformations and the energy shift of the dual field theory state. We show that the Bäcklund transformations can be represented as a finite-time evolution generated by a special linear combination of the Pohlmeyer charges. This is a manifestation of the general property of Bäcklund transformations known as spectrality. We also discuss the plane wave limit

    Double valley Dirac fermions for 3D and 2D Hg1x_{1-x}Cdx_xTe with strong asymmetry

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    In this paper the possibility to bring about the double- valley Dirac fermions in some quantum structures is predicted. These quantum structures are: strained 3D Hg1x_{1-x}Cdx_xTe topological insulator (TI) with strong interface inversion asymmetry and the asymmetric Hg1x_{1-x}Cdx_xTe double quantum wells (DQW). The numerical analysis of the dispersion relation for 3D TI Hg1x_{1-x}Cdx_xTe for the proper Cd (xx)-content of in the Hg1x_{1-x}Cdx_xTe-compound clearly show that the inversion symmetry breaking together with the unaxial tensile strain causes splitting each of Dirac nodes (two belonging to two interfaces) into two in the proximity of Γ\Gamma-point. The similar effects can be obtained for asymmetric Hg1x_{1-x}Cdx_xTe DQW with the proper content of Cd and proper width of the quantum wells. The aim of this work is to explore the inversion symmetry breaking in 3D TI and 2D DQWs mixed HgCdTe-systems. It is shown that this symmetry breaking leads to the dependence of carriers energy vs quasi-momentum similar to that of Weyl fermions.Comment: arXiv admin note: text overlap with arXiv:1605.09214 by other author

    Spatiotemporal pattern formation in a three-variable CO oxidation reaction model

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    The spatiotemporal pattern formation is studied in the catalytic carbon monoxide oxidation reaction that takes into account the diffusion processes over the Pt(110) surface, which may contain structurally different areas. These areas are formed during CO-induced transition from a reconstructed phase with 1×21\times2 geometry of the overlayer to a bulk-like (1×11\times1) phase with square atomic arrangement. Despite the CO oxidation reaction being non-autocatalytic, we have shown that the analytic conditions of the existence of the Turing and the Hopf bifurcations can be satisfied in such systems. Thus, the system may lose its stability in two ways --- either through the Hopf bifurcation leading to the formation of temporal patterns in the system or through the Turing bifurcation leading to the formation of regular spatial patterns. At a simultaneous implementation of both scenarios, spatiotemporal patterns for CO and oxygen coverages are obtained in the system.Comment: 11 pages, 6 figures, 1 tabl

    Analysis of some localized boundary-domain integral equations for transmission problems with variable coefficients

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    This is the post-print version of the Article. The official published version can be found at the links below - Copyright @ 2011 Birkhäuser Boston.Some segregated systems of direct localized boundary-domain integral equations (LBDIEs) associated with several transmission problems for scalar PDEs with variable coefficients are formulated and analyzed for a bounded domain composed of two subdomains with a coefficient jump over the interface. The main results established in the paper are the LBDIE equivalence to the original transmission problems and the invertibility of the corresponding localized boundary-domain integral operators in corresponding Sobolev spaces function spaces.This research was supported by the EPSRC grant EP/H020497/1: ”Mathematical analysis of Localized Boundary-Domain Integral Equations for Variable-Coefficient Boundary Value Problems” and partly by the Georgian Technical University grant in the case of the third author

    On complete integrability of the Mikhailov-Novikov-Wang system

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    We obtain compatible Hamiltonian and symplectic structure for a new two-component fifth-order integrable system recently found by Mikhailov, Novikov and Wang (arXiv:0712.1972), and show that this system possesses a hereditary recursion operator and infinitely many commuting symmetries and conservation laws, as well as infinitely many compatible Hamiltonian and symplectic structures, and is therefore completely integrable. The system in question admits a reduction to the Kaup--Kupershmidt equation.Comment: 5 pages, no figure
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