arXiv subjects

I. S. Gandzha

Publications and source records attributed to I. S. Gandzha.

8 recordsLinked to original sources

arXiv2022

Hamiltonian form of extended cubic-quintic nonlinear Schrödinger equation in a nonlinear Klein-Gordon model

We derive an extended cubic-quintic nonlinear Schrödinger equation with Hamiltonian structure in a nonlinear Klein-Gordon model with cubic-quintic nonlinearity. We use the nonlinear dispersion relation to properly take into account the input of high-order nonlinear effects in the Hamiltonian perturbation approach to nonlinear modulation. We demonstrate that changing the balance between the cubic and quintic nonlinearities has a significant effect on the stability of unmodulated wave packets to long-wave modulations.

nlin.PS↗

arXiv2021

Modeling and Controlling the Spread of Epidemic with Various Social and Economic Scenarios

We propose a dynamical model for describing the spread of epidemics. This model is an extension of the SIQR (susceptible-infected-quarantined-recovered) and SIRP (susceptible-infected-recovered-pathogen) models used earlier to describe various scenarios of epidemic spreading. As compared to the basic SIR model, our model takes into account two possible routes of contagion transmission: direct from the infected compartment to the susceptible compartment and indirect via some intermediate medium or fomites. Transmission rates are estimated in terms of average distances between the individuals in selected social environments and characteristic time spans for which the individuals stay in each of these environments. We also introduce a collective economic resource associated with the average amount of money or income per individual to describe the socioeconomic interplay between the spreading process and the resource available to infected individuals. The epidemic-resource coupling is supposed to be of activation type, with the recovery rate governed by the Arrhenius-like law. Our model brings an advantage of building various control strategies to mitigate the effect of epidemic and can be applied, in particular, to modeling the spread of COVID-19.

physics.soc-ph↗

arXiv2020

Epidemic-Driven Collapse in a System with Limited Economic Resource. II

We consider a possibility of socioeconomic collapse caused by the spread of epidemic. To this end, we exploit a simple SIS-like (susceptible-infected-susceptible) model with negative feedback between the infected population size and a collective economic resource associated with the average amount of money or income per economic agent. The coupling mechanism in such a system is supposed to be of activation type, with the recovery rate governed by the Arrhenius-like law. In this case, economic resource formally plays the role of effective market temperature and the minimum level of resource consumption is associated with activation energy. Such a coupling can result in the collapsing effect opposite to thermal explosion, so that the epidemic could ultimately drive the system to a collapse at nonzero activation energy because of the limited resource. In this case, the system can no longer stabilize and return to the stable pre-epidemic state or a poorer post-epidemic state. We demonstrate that the system's collapse can partially be mitigated by external subsidies meaning constant resource inflow from some external source or by means of debt interpreted as a negative resource. We also consider a simple quarantine scenario and show that it can lead to different socioeconomic outcomes, depending on initial resource (market temperature) and the minimum level of resource consumption (activation energy).

physics.soc-ph↗

arXiv2020

The Epidemic-Driven Collapse in a System with Limited Economic Resource

We consider a possibility of socioeconomic collapse caused by the spread of epidemic in a basic dynamical model with negative feedback between the infected population size and a formal collective economic resource. The epidemic-resource coupling is supposed to be of activation type, with the recovery rate governed by the Arrhenius-like law and resource playing the role of temperature. Such a coupling can result in the collapsing effect opposite to thermal explosion because of the limited resource. In this case, the system can no longer stabilize and return to the stable pre- or post-epidemic states. We demonstrate that such a collapse can partially be mitigated by means of a negative resource or debt.

physics.soc-ph↗

arXiv2020

High-order nonlinear Schrödinger equation for the envelope of slowly modulated gravity waves on the surface of finite-depth fluid and its quasi-soliton solutions

We consider the high-order nonlinear Schrödinger equation derived earlier by Sedletsky [Ukr. J. Phys. 48(1), 82 (2003)] for the first-harmonic envelope of slowly modulated gravity waves on the surface of finite-depth irrotational, inviscid, and incompressible fluid with flat bottom. This equation takes into account the third-order dispersion and cubic nonlinear dispersive terms. We rewrite this equation in dimensionless form featuring only one dimensionless parameter $kh$, where $k$ is the carrier wavenumber and $h$ is the undisturbed fluid depth. We show that one-soliton solutions of the classical nonlinear Schrödinger equation are transformed into quasi-soliton solutions with slowly varying amplitude when the high-order terms are taken into consideration. These quasi-soliton solutions represent the secondary modulations of gravity waves.

nlin.PS↗

arXiv2015

The effect of the fifth-order nonlinearity on the existence of bright solitons below the modulation instability threshold

We analyze three different high-order nonlinear Schrödinger equation (HONLSE) models that have been used in the literature to describe the evolution of slowly modulated gravity waves on the surface of ideal finite-depth fluid. We demonstrate that the inclusion of the fifth-order nonlinear term to the HONLSE model introduces only a small correction to the amplitude of the bright HONLSE soliton solutions obtained without this term. Such soliton slutions behave as quasi-solitons in this more general case.

nlin.PS↗

arXiv2015

Bright and Dark Solitons on the Surface of Finite-Depth Fluid Below the Modulation Instability Threshold

We use the high-order nonlinear Schrödinger equation (NLSE) derived to model the evolution of slowly modulated wave trains with narrow spectrum on the surface of ideal finite-depth fluid. This equation is the finite-depth counterpart of celebrated Dysthe's equation, which is usually used for the same purpose in the case of infinite depth. We demonstrate that this generalized equation admits bright soliton solutions for depths below the modulation instability threshold $kh\approx 1.363$ ($k$ being the carrier wave number and $h$ the undisturbed fluid depth), which is not possible in the case of standard NLSE. These bright solitons can exist along with the dark solitons that have recently been observed in a water wave tank [Phys. Rev. Lett. 110, 124101 (2013)].

nlin.PS↗

arXiv2009

Two-Parameter Method for Describing the Nonlinear Evolution of Narrow-Band Wave Trains

We consider the evolution of narrow-band wave trains of finite amplitude in a nonlinear dispersive system which is described by the Klein--Gordon equation with arbitrary polynomial nonlinearity. We use a new perturbative technique which allows the original wave equation to be reduced to a model equation for the wave train envelope (high-order nonlinear Schrödinger equation). The time derivative is expanded into an asymptotic series in two independent parameters which characterize the smallness of amplitudes ($\varepsilon$) and the slowness of their spatial variations ($μ$). In contrast to other perturbative methods in which these two parameters are taken equal (e.g., the multiple scale method), the two-parameter method produces no secular terms. The results of this study can be applied to investigating the propagation of ultrashort (femtosecond) pulses in optical fibers, to studying the wave events on a fluid surface, and to describing the Langmuir waves in hot plasmas.

nlin.PS↗