Higher-order nonlinear modes and bifurcation phenomena due to degenerate parametric four-wave mixing

We demonstrate that weak parametric interaction of a fundamental beam with its third harmonic field in Kerr media gives rise to a rich variety of families of non-fundamental (multi-humped) solitary waves. Making a comprehensive comparison between bifurcation phenomena for these families in bulk media and planar waveguides, we discover two novel types of soliton bifurcations and other interesting findings. The later includes (i) multi-humped solitary waves without even or odd symmetry and (ii) multi-humped solitary waves with large separation between their humps which, however, may not be viewed as bound states of several distinct one-humped solitons.Comment: 9 pages, 17 figures, submitted to Phys. Rev.

Closed extended r-spin theory and the Gelfand–Dickey wave function

We study a generalization of genus-zero r-spin theory in which exactly one insertion has a negative-one twist, which we refer to as the “closed extended” theory, and which is closely related to the open r-spin theory of Riemann surfaces with boundary. We prove that the generating function of genus-zero closed extended intersection numbers coincides with the genus-zero part of a special solution to the system of differential equations for the wave function of the rth Gelfand–Dickey hierarchy. This parallels an analogous result for the open r-spin generating function in the companion paper Buryak et al. (2018) to this work

Scientific rationale for inclusion of a new nature complex Belyj Kolodez (Russia, Belgorod Region) into the emerald network

The article shows that there are resources for extending the national list of potential Areas of Special Conservation Interest (ASCI's) of the Emerald network in densely populated and old-developed regions. The representativeness of the Belyj Kolodez nature complex (Russia, Belgorod region) is substantiated. Based on the survey of the territory, the types of priority habitats were identified according to the EUNIR classificatio

A remark on deformations of Hurwitz Frobenius manifolds

In this note we use the formalism of multi-KP hierarchies in order to give some general formulas for infinitesimal deformations of solutions of the Darboux-Egoroff system. As an application, we explain how Shramchenko's deformations of Frobenius manifold structures on Hurwitz spaces fit into the general formalism of Givental-van de Leur twisted loop group action on the space of semi-simple Frobenius manifolds.Comment: 10 page

Solutions to the Optical Cascading Equations

Group theoretical methods are used to study the equations describing \chi^{(2)}:\chi^{(2)} cascading. The equations are shown not to be integrable by inverse scattering techniques. On the other hand, these equations do share some of the nice properties of soliton equations. Large families of explicit analytical solutions are obtained in terms of elliptic functions. In special cases, these periodic solutions reduce to localized ones, i.e., solitary waves. All previously known explicit solutions are recovered, and many additional ones are obtainedComment: 21 page

The infrastructure of land management in the post-antique agrolandscapes of Crimea = Инфраструктура землеустройства в постантичных агроландшафтах Крыма

Результаты комплексных исследований древнего землеустройства и землепользования вблизи археологических памятников античного времени в Северо-Западном Крым

Approximate solutions and scaling transformations for quadratic solitons

We study quadratic solitons supported by two- and three-wave parametric interactions in chi-2 nonlinear media. Both planar and two-dimensional cases are considered. We obtain very accurate, 'almost exact', explicit analytical solutions, matching the actual bright soliton profiles, with the help of a specially-developed approach, based on analysis of the scaling properties. Additionally, we use these approximations to describe the linear tails of solitary waves which are related to the properties of the soliton bound states.Comment: 11 pages, 9 figures; submitted for publicatio

Model of position-dynamic structure of river basins

In this work, we have presented semi automated means of modeling of position-dynamic structure (PDS) of river basins’ landscapes with application of geo-informational systems (GIS). Results of modeling were tested on the basin of one of headwaters. The structure of the model includes landscape lines, layers, sub-regions and regions. The model takes into account conditions of formation of landscape’s PDS in mountain and plain parts of river basinsyesБелгородский государственный университе

Refined open intersection numbers and the Kontsevich-Penner matrix model

A study of the intersection theory on the moduli space of Riemann surfaces with boundary was recently initiated in a work of R. Pandharipande, J.P. Solomon and the third author, where they introduced open intersection numbers in genus 0. Their construction was later generalized to all genera by J.P. Solomon and the third author. In this paper we consider a refinement of the open intersection numbers by distinguishing contributions from surfaces with different numbers of boundary components, and we calculate all these numbers. We then construct a matrix model for the generating series of the refined open intersection numbers and conjecture that it is equivalent to the Kontsevich-Penner matrix model. An evidence for the conjecture is presented. Another refinement of the open intersection numbers, which describes the distribution of the boundary marked points on the boundary components, is also discussed