Narrow Results

We study the propagation of nonlinear waves in a three-component reaction–diffusion system. The problem of the existence of the stationary pulse-like solutions is reduced to the analysis of homoclinic trajectories of a fourth-order system of nonlinear ODEs. We have obtained the parameter set corresponding to the homoclinic bifurcations that defines the velocity spectra of the traveling pulses. We have shown that the pulses behave like autowaves annihilating in head-on collision and like dissipative solitons crossing each other, reflecting at boundaries. We have provided a qualitative explanation for such a behavior.

In this paper, we discussed the longitudinal harmonic waves reflection from a solid elastic half-space with electromagnetic and gravity fields influence, considering a fractional order via fractional exponential function method. The clarifications are required for the reflection amplitudes ratios (i.e. the ratios between the reflected waves amplitude and the incident waves amplitude). The results obtained were calculated analytically and displayed by graphs to show the physical meaning of the phenomenon. A comparison has been made between the fractional and integer derivatives. The results of this paper demonstrate the rigor and effectiveness of the considered fractional technique.

This study indicates that the removal of reflections from T-ray signals can be carried out in the frequency domain without prior knowledge of material parameters or sample thickness. By fitting polynomials to the logarithm and the argument of the sample's transfer function, the Fabry-Pérot reflection term is canceled out, leading to disappearance of the reflections in spatial domain. The method successfully removes the reflections for optically thick samples under the condition of noise or amplitude fluctuations. The application to optically thin samples is possible when the samples are subjected to broadband terahertz measurements. The Fabry-Pérot free signal, when used as input to the parameter estimation method, results in correct material parameters with low variance.