Valery S. Shchesnovich

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The perturbation theory based on the Riemann-Hilbert problem is developed for the modified nonlinear Schrödinger equation which describes the propagation of femtosecond optical pulses in nonlinear single-mode optical fibers. A detailed analysis of the adiabatic approximation to perturbation-induced evolution of the soliton parameters is given. The linear(More)
We study Zener tunneling in two-dimensional photonic lattices and derive, for the case of hexagonal symmetry, the generalized Landau-Zener-Majorana model describing resonant interaction between high-symmetry points of the photonic spectral bands. We demonstrate that this effect can be employed for the generation of Floquet-Bloch modes and verify the model(More)
We use the Riemann-Hilbert problem to study the interaction of the soliton with radiation in the parametrically driven, damped nonlinear Schrödinger equation. The analysis is reduced to the study of a finite-dimensional dynamical system for the amplitude and phase of the soliton and the complex amplitude of the long-wavelength radiation. In contrast to(More)
We derive the soliton matrices corresponding to an arbitrary number of higher-order normal zeros for the matrix Riemann–Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order soli-tons. Our soliton matrices explicitly give all higher-order multisoliton solutions to the nonlinear partial differential(More)
We explore the conditions under which identical particles in unitary linear networks behave as the other species, i.e. bosons as fermions and fermions as bosons. It is found that the Boson-Sampling computer of Aaronson & Arkhipov can be implemented in an interference experiment with non-interacting fermions in an appropriately entangled state. Moreover, a(More)
We discuss the interband light tunneling in a two-dimensional periodic photonic structure, as studied recently in experiments for optically induced photonic lattices [Trompeter, Phys. Rev. Lett. 96, 053903 (2006)]. We identify the Zener tunneling regime at the crossing of two Bloch bands, which occurs in the generic case of a Bragg reflection when the Bloch(More)
We study the closeness of an experimental unitary bosonic network with only partially indistinguishable bosons in an arbitrary mixed input state, in particular an experimental realization of the Boson-Sampling computer, to the ideal bosonic network, where the measure of closeness of two networks is the trace distance between the output probability(More)
We study, analytically and numerically, the dynamics of interband transitions in two-dimensional hexagonal periodic photonic lattices. We develop an analytical approach employing the Bragg resonances of different types and derive the effective multi-level models of the Landau-Zener-Majorana type. For two-dimensional periodic potentials without a tilt, we(More)
It is found that identical bosons (fermions) show a generalized bunching (antibunching) property in linear networks: the absolute maximum (minimum) of the probability that all N input particles are detected in a subset of K output modes of any nontrivial linear M-mode network is attained only by completely indistinguishable bosons (fermions). For fermions K(More)