Results of numerical simulations are presented for propagation of solitary waves in an elastic rod of positive or negative Poisson's ratio, i.e. of a common or auxetic material. Splitting of various initial pulses during propagation into a sequence of solitary waves is considered in frames of a model which contains both quadratic and cubic nonlinear terms. The obtained results are compared with some exact analytic solutions, called solitons, what leads to the conclusion that the solitons describe well the more complicated wave fields which are obtained by numerical simulations. This is because the analytic solutions reflect complete balance between various orders of nonlinearity and dispersion. Collisions between some obtained solitary waves are also presented.

Special soliton analytical solutions are seeked for the so-called double dispersion equation (or Porubov's equation), which describes the propagation of longitudinal waves in an elastic rod. Using the F-expansion method, a new interesting class of traveling solitary waves is obtained. As a byproduct, the results obtained by other authors for some special cases are regained. Some numerical simulations are also performed. Splitting of various initial pulses during propagation into a sequence of solitary waves is considered. The dependence of the amplitude and the velocity of the solitary waves on Poisson's ratio is discussed in detail. Collisions between some obtained solitary waves are also presented. The simulation results are compared with the obtained exact analytical solutions-the latter reflect the perfect balance between the nonlinearity and dispersion. The comparison indicates that the obtained exact solutions are useful for describing more complicated wave fields studied by numerical simulations. It also indicates that the numerical results for auxetic materials are in better agreement with theoretical solutions than in the case of ordinary materials. Furthermore, one can conclude that the Secant pulse generates solitary waves closer to the analytical predictions than a Gaussian pulse. This is similar to the case of variational method, where the Secant trial function is also more proper than the Gaussian one.

Abstract.A Λ-like model of atomic levels involving two auto-ionizing states is considered. The levels are irradiated by two external electromagnetic fields, a strong driving and a weak probing ones. The analytical formula for medium susceptibility shows an additional electromagnetically induced transparency window caused by the second auto-ionizing level. Characteristics of both transparency windows are analyzed depending on parameters of auto-ionizing levels and the external driving field. Manipulation of these characteristics seems to be very effective because of their large sensitivity with respect to the parameters involved in the problem. This manipulation becomes even more feasible when considered model is implemented in so-called laser-induced continuum structure.

Octave spanning all-normal dispersion supercontinuum generation (SCG) was experimentally demonstrated in a solid, suspended-core fiber (SCF) infiltrated with water. Replacement of air with water in the cladding air-holes leads to a dramatic modification of the dispersion profile of the fiber, significantly flattening the characteristic over the visible and much of the near-infrared wavelength range at normal values. In such a fiber infiltrated with water, all-normal dispersion supercontinuum was generated with the spectral coverage from 435 nm to 1330 nm using femtosecond pumping with the output peak power of 150 kW and 800 nm central wavelength. The SCF without water infiltration – air in the cladding region – had a zero-dispersion wavelength at 760 nm and enabled the generation of the anomalous dispersion dynamics-based SCG in the wavelength range from 450 nm to 1250 nm. We also numerically calculated the coherence of simulated supercontinuum pulses with one-photon-per-mode noise seeds and point out that the all-normal dispersion SCG in suspended-core fiber infiltrated with water has the potential for high temporal coherence, while the fiber without water infiltration shows gradual decoherence of generated supercontinuum pulses with increasing pump power, over similar peak power range.

In this paper we consider a generalized double dispersion equation of Porubov's type 4,5 . which describes the propagation of the longitudinal strain waves in the rod. By analogy with the optical case 2 , the higher orders of nonlinearity have been included which leads to an interesting class of traveling solitary waves for both cases: without cubic nonlinearity and with its presence. The F-expansion method described in 3 has been used. As a byproduct, we obtain the results given previously by other authors 4,5 . It will be shown that our analytical solutions describe very well the results obtained by numerical simulations 6 .

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In this paper, using the idea introduced in [1] and developed in [2] we consider the influence of collisional fluctuations on the Mollow spectra of resonance fluorescence (RF). The fluctuations are taken into account by a simple shift of the constant detuning, involved in a set of optical Bloch equations by collision frequency noise which is modelled by a two-step random telegraph signal (RTS).We consider in detail the Mollow spectra for RF in the case of an arbitrary detuning of the laser frequency, where the emitter is a member of a statistical ensemble in thermodynamic equilibrium with the buffer gas at temperature T which is treated as a colored environment, and velocity v is distributed with the Maxwell-Boltzmann density.

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