Exact Moving and Stationary Solutions of a Generalized Discrete Nonlinear Schrodinger Equation

We obtain exact moving and stationary, spatially periodic and localized solutions of a generalized discrete nonlinear Schr\"odinger equation. More specifically, we find two different moving periodic wave solutions and a localized moving pulse solution. We also address the problem of finding exact stationary solutions and, for a particular case of the model when stationary solutions can be expressed through the Jacobi elliptic functions, we present a two-point map from which all possible stationary solutions can be found. Numerically we demonstrate the generic stability of the stationary pulse solutions and also the robustness of moving pulses in long-term dynamics.Comment: 22 pages, 7 figures, to appear in J. Phys.

The anisotropic Heisenberg chain in coexisting transverse and longitudinal magnetic fields

The one-dimensional spin-1/2 $XXZ$ model in a mixed transverse and longitudinal magnetic field is studied. Using the specially developed version of the mean-field approximation the order-disorder transition induced by the magnetic field is investigated. The ground state phase diagram is obtained. The behavior of the model in low transverse field is studied on the base of conformal field theory. The relevance of our results to the observed phase transition in the quasi-one-dimensional antiferromagnet $Cs_2 Co Cl_4$ is discussed.Comment: 18 pages, 6 figure

Multi-field approach in mechanics of structural solids

We overview the basic concepts, models, and methods related to the multi-field continuum theory of solids with complex structures. The multi-field theory is formulated for structural solids by introducing a macrocell consisting of several primitive cells and, accordingly, by increasing the number of vector fields describing the response of the body to external factors. Using this approach, we obtain several continuum models and explore their essential properties by comparison with the original structural models. Static and dynamical problems as well as the stability problems for structural solids are considered. We demonstrate that the multi-field approach gives a way to obtain families of models that generalize classical ones and are valid not only for long-, but also for short-wavelength deformations of the structural solid. Some examples of application of the multi-field theory and directions for its further development are also discussed.Comment: 25 pages, 18 figure

Angular distributions in J/ψ→ppˉπ0(η)J/\psi\to p\bar{p}\pi^{0}(\eta) decays

The differential decay rates of the processes $J/\psi\to p\bar{p}\pi^{0}$ and $J/\psi\to p\bar{p}\eta$ close to the $p\bar{p}$ threshold are calculated with the help of the $N\bar{N}$ optical potential. The same calculations are made for the decays of $\psi(2S)$. We use the potential which has been suggested to fit the cross sections of $N\bar{N}$ scattering together with $N\bar{N}$ and six pion production in $e^{+}e^{-}$ annihilation close to the $p\bar{p}$ threshold. The $p\bar{p}$ invariant mass spectra is in agreement with the available experimental data. The anisotropy of the angular distributions, which appears due to the tensor forces in the $N\bar{N}$ interaction, is predicted close to the $p\bar{p}$ threshold. This anisotropy is large enough to be investigated experimentally. Such measurements would allow one to check the accuracy of the model of $N\bar{N}$ interaction.Comment: 10 pages, 8 figure

Wave scattering on a domain wall in a chain of PT-symmetric couplers

We study wave propagation in linear arrays composed of pairs of conjugate waveguides with balanced gain and loss, i.e. arrays of the PT-symmetric couplers, where the linear spectrum is known to feature high-frequency and low-frequency branches. We introduce a domain wall by switching the gain and loss in a half of the array, and analyze the scattering of linear waves on this defect. The analysis reveals two major effects: amplification of both reflected and transmitted waves, and excitation of the reflected and transmitted low-frequency and high-frequency waves by the incident high-frequency and low-frequency waves, respectively.Comment: 7 pages, 9 figures, Physical Review A, in pres