Statistical approach of the modulational instability of the discrete self-trapping equation

The discrete self-trapping equation (DST) represents an useful model for several properties of one-dimensional nonlinear molecular crystals. The modulational instability of DST equation is discussed from a statistical point of view, considering the oscillator amplitude as a random variable. A kinetic equation for the two-point correlation function is written down, and its linear stability is studied. Both a Gaussian and a Lorentzian form for the initial unperturbed wave spectrum are discussed. Comparison with the continuum limit (NLS equation) is done.Comment: 10 page

On the Lattice Corrections to the Free Energy of Kink-Bearing Nonlinear One-Dimensional Scalar Systems

A ri proof of the effective potential (lattice corrections included) deduced by Trullinger and Sasaki is given. Using asymptotic methods from the theory of differential equations depending on a large parameter, the lattice corrections to the kink and kink-kink contributions to the free energy are calculated. The results are in complete agreement with a first order correction to the energy of the static kink.Comment: 12 pages,plainte

On a class of rational and mixed soliton-rational solutions of Toda lattice

A class of rational solutions of Toda lattice satisfying certain Backlund transformations and a class of mixed rational-soliton solutions (quasisolitons) in wronskian formare obtained using the method of Ablowitz and Satsuma. Also an extended class of rational solutions are found using an appropriate recursion relation. They are also solutions of Boussinesq equation and it is conjectured that there is a larger class of common solutions of both equations.Comment: 10 pages, Late

The reasons of migration of rural youth

Рассматриваются причины оттока современной российской молодежи в крупные города. В качестве значимых факторов выделяются низкие шансы в реализации образовательной и профессиональной стратегий, невозможность удовлетворения социальных и культурных запросов, поддержания современных стандартов жизни.The reasons of modern Russian youth outflow in big cities. As significant factors stand out in the low odds of realization of educational and professional strategies, inability to meet the social and cultural needs, maintaining modern living standards