arXiv subjects

Shaykin Dmitriy

Publications and source records attributed to Shaykin Dmitriy.

3 recordsLinked to original sources

arXiv2025

Solitons in a one-dimensional rhombic waveguide array

Two types of soliton solutions are analytically considered in a rhombic onedimensional lattice: transverse (discrete) solitons and longitudinal solitons. Based on the multi-scale method, longitudinal solitons are obtained as envelopes of wave packets outside the forbidden gap, on the gap and under the gap. A discrete soliton was obtained based on a wave packet from the center of the Brillouin zone. The numerical calculations are in good agreement with the analytical predictions.

nlin.PS↗

arXiv2025

Analysis of modulated linear wave packets and gap solitons in coupled optical fibers

A coupled pair of waveguides with refractive indices of different signs is considered. It is shown that the gap in the linear wave spectrum closes if these waves are amplitude modulated. To look for solitons as envelopes of exponentially modulated wave packets, the dispersion law of these packets is used. Different decompositions of the dispersion law lead to solutions related to different parts of the spectrum. Numerical calculations demonstrate a good agreement with analytical predictions.

physics.optics↗

arXiv2025

Propagation of narrow and fast solitons through dispersive shock waves in hydrodynamics of simple waves

We study the propagation of narrow solitons through various profiles of dispersive shock waves (DSW) for the generalized Korteweg-de Vries equation. We consider situations in which the soliton passes through the DSW region quickly enough and does not get trapped in it. The idea is to consider the motion of such solitons through DSW as motion along some smooth effective profile. In the case of KdV and modified KdV, based on the law of conservation of momentum and the equation of motion, this idea is proven rigorously; for other cases of generalized KdV, we take this as a natural generalization. In specific cases of self-similar decays for KdV and modified KdV, a method for selecting an effective field is demonstrated. For the case of generalized KdV, a hypothesis is proposed for selecting an effective field for any wave pulse that is not very large compared to the soliton. All proposed suggestions are numerically tested and demonstrate a high accuracy of reliability.

nlin.PS↗