Statistics of a noise-driven Manakov soliton

We investigate the statistics of a vector Manakov soliton in the presence of additive Gaussian white noise. The adiabatic perturbation theory for Manakov soliton yields a stochastic Langevin system which we analyze via the corresponding Fokker-Planck equation for the probability density function (PDF) for the soliton parameters. We obtain marginal PDFs for the soliton frequency and amplitude as well as soliton amplitude and polarization angle. We also derive formulae for the variances of all soliton parameters and analyze their dependence on the initial values of polarization angle and phase.Comment: Submitted to J.Phys.A: Mathematical and Genera

Darboux transformations of coherent states of the time-dependent singular oscillator

Darboux transformation of both Barut-Girardello and Perelomov coherent states for the time-dependent singular oscillator is studied. In both cases the measure that realizes the resolution of the identity operator in terms of coherent states is found and corresponding holomorphic representation is constructed. For the particular case of a free particle moving with a fixed value of the angular momentum equal to two it is shown that Barut-Giriardello coherent states are more localized at the initial time moment while the Perelomov coherent states are more stable with respect to time evolution. It is also illustrated that Darboux transformation may keep unchanged this different time behavior.Comment: 13 page

Composite bound states of wide and narrow envelope solitons in the coupled Schrödinger equations through matched asymptotic expansions

Coupled nonlinear Schrödinger equations, linked by cross modulation terms, arise in both nonlinear optics and in Rossby waves in the atmosphere and ocean. Numerically, Akhmediev and Ankiewicz and Haelterman and Sheppard discovered a class of soiltary waves which are composed of a tall, narrow sech-shaped soliton in one mode, bound to a pair of short, wide sech-shaped peaks in the other mode or polarization. Through the method of matched asymptotic expansions, we derive analytical approximations to these solitary waves, and to their periodic generalization, which have been hitherto accessible only through numerical computation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/49070/2/no9601.pd

RESEARCH OF INFLUENCE OF LIQUID ALUMINUM ON RESISTANCE OF THE STEEL AND CAST-IRON TOOL

The study of the interaction of steel and cast iron with aluminum was performed by immersion, and isothermal holding. By optical and electron microscopy, the microstructure of the reaction zone was investigated. The partial enthalpy of dissolution of iron, steel and cast iron in liquid aluminum has been investigated by high-temperature calorimetry at 1773 K. X-ray analysis and microhardness measurements was used to study the phase composition of the reaction zone. The thermodynamic descriptions of the system Al–Fe and Al–C–Fe are performed within the CALPHAD-method