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.

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.

A toy model for the epidemic-driven collapse in a system with limited economic resource.

Abstract: Based on a toy model for a trivial socioeconomic system, we demonstrate that the activation-type mechanism of the epidemic-resource coupling can lead to the collapsing effect opposite to thermal explosion. We exploit a SIS-like (susceptible-infected-susceptible) model coupled with the dynamics of average economic resource for a group of active economic agents. The recovery rate of infected individuals is supposed to obey the Arrhenius-like law, resulting in a mutual negative feedback between the number of active agents and resource acquisition.

Relationship between the Hamiltonian and non-Hamiltonian forms of a fourth-order nonlinear Schrödinger equation.

We show the equivalence between the Hamiltonian and non-Hamiltonian forms of a fourth-order nonlinear Schrödinger equation for a particular example of the physical system described by the nonlinear Klein-Gordon equation with cubic nonlinearity.

Steep sharp-crested gravity waves on deep water.

A new type of steep two-dimensional irrotational symmetric periodic gravity wave with local singular point inside the flow domain is revealed on inviscid incompressible fluid of infinite depth. The speed of fluid particles in the vicinity of the crest of these waves is greater than their phase speed. Corresponding particle trajectories provide insight into how gravity waves overturn and break.