Bottom pressure distribution under a solitonic wave reflecting on a vertical wall
European Journal of Mechanics - B/Fluids. 2014. Vol. 48. P. 13-18.
Pelinovsky E., Touboil J.
The bottom pressure distribution under solitonic waves, travelling or fully reflected at a wall is analysed here. Results given by two kind of numerical models are compared. One of the models is based on the Green–Naghdi equations, while the other one is based on the fully nonlinear potential equations. The two models differ through the way in which wave dispersion is taken into account. This approach allows us to emphasize the influence of dispersion, in the case of travelling or fully reflected waves. The Green–Naghdi model is found to predict well the bottom pressure distribution, even when the quantitative representation of the runup height is not satisfactorily described.
Research target: MathematicsPhysics
Priority areas: mathematicsengineering science
Keywords: solitons
Heat operator with pure soliton potential: properties of the Jost and dual Jost solutions
Boiti M., Pempinelli F., Pogrebkov A. Journal of Mathematical Physics. 2011. Vol. 52. No. 083506. P. 1-21.
Properties of Jost and dual Jost solutions of the heat equation, F (x,k) and Y(x,k), in the case of a pure solitonic potential are studied in detail.We describe their analytical properties on the spectral parameter k and their asymptotic behavior on the x-plane and we show that the values of e(−qx)F (x, k) and the residues of exp(qx )Y(x,k) at special discrete values of k are bounded functions of x in a polygonal region of the q-plane. Correspondingly, we deduce that the extended version L(q) of the heat operator with a pure solitonic potential has left and right annihilators for q belonging to these polygonal regions.
Perspective Methods of Transferring Information via Optical Communication Channels
Isaev E., Tarasov P. A. In bk.: Breakthrough Directions of Scientific Research in NRNU MEPhI: Development Perspectives in the Framework of the Strategic. Vol. 2018. KNE PUBLISHING, 2018. P. 136-143.
Perspective methods of information transfer in optical communication channels based on the latest achievements of quantum physics are considered. In the near future these methods can solve both the problem of creating an optical channel conducting with physically unlimited bandwidth, and the problem of secretly transferring information in a fiber-optic information channel. The results of the latest experiments related to the quantum properties of photons are described. The use of solitons as carriers of an information signal is considered. The technologies of using the " temporal cloak " and noise of optical amplifiers for data transmission in fiber-optic communication lines are presented.
Коротковолновые поперечные неустойчивости плоских солитонов в двумерном гиперболическом нелинейном уравнении Шредингера
Пелиновский Д. Е., Рувинская Е. А., Куркина О. Е. и др. Теоретическая и математическая физика. 2014. Т. 179. № 1. С. 78-89.
We prove that line solitons of the two-dimensional hyperbolic nonlinear Schr¨odinger equation are unstable under transverse perturbations of arbitrarily small periods, i.e., short waves. The analysis is based on the construction of Jost functions for the continuous spectrum of Schr¨odinger operators, the Sommerfeld radiation conditions, and the Lyapunov–Schmidt decomposition. We derive precise asymptotic expressions for the instability growth rate in the limit of short periods.
Higher-order (2+4) Korteweg-de Vries - like equation for interfacial waves in a symmetric three-layer fluid
O.E. Kurkina, A.A. Kurkin, T. Soomere et al. Physics of Fluids. 2011. Vol. 23. No. 11. P. 116602-1-13-116602-13.
We address a specific but possible situation in natural water bodies when the three-layer stratification has a symmetric nature, with equal depths of the uppermost and the lowermost layers. In such case, the coefficients at the leading nonlinear terms of the modified Korteweg-de Vries (mKdV) equation vanish simultaneously. It is shown that in such cases there exists a specific balance between the leading nonlinear and dispersive terms. An extension to the mKdV equation is derived by means of combination of a sequence of asymptotic methods. The resulting equation contains a cubic and a quintic nonlinearity of the same magnitude and possesses solitary wave solutions of different polarity. The properties of smaller solutions resemble those for the solutions of the mKdV equation whereas the height of the taller solutions is limited and they become table-like. It is demonstrated numerically that the collisions of solitary wave solutions to the resulting equation are weakly inelastic: the basic properties of the counterparts experience very limited changes but the interactions are certainly accompanied by a certain level of radiation of small-amplitude waves.
Self-similar potentials in quantum mechanics and coherent states
Spiridonov V. Cornell University Library, 2020
A brief description of the relations between the factorization method in quantum mechanics, self-similar potentials, integrable systems and the theory of special functions is given. New coherent states of the harmonic oscillator related to the Fourier transformation are constructed.
Soliton equations and the Riemann-Schottky problem
Krichever I. M., Schiota T. In bk.: Handbook of Moduli. Vol. II. Boston: International Press of Boston Inc, 2013.
Novikov's conjecture on the Riemann-Schottky problem: {\it the Jacobians of smooth algebraic curves are precisely those indecomposable principally polarized abelian varieties (ppavs) whose theta-functions provide solutions to the Kadomtsev-Petviashvili (KP) equation}, was the first evidence of nowadays well-established fact: connections between the algebraic geometry and the modern theory of integrable systems is beneficial for both sides. The purpose of this paper is twofold. Our first goal is to present a proof of the strongest known characterization of a Jacobian variety in this direction: {\it an indecomposable ppav X is the Jacobian of a curve if and only if its Kummer variety K(X) has a trisecant line} and the solution of the characterization problem of principally polarized Prym varieties. The latter problem is almost as old and famous as the Riemann-Schottky problem but is much harder. In some sense the Prym varieties may be geometrically the easiest-to-understand ppavs beyond Jacobians, and studying them may be a first step towards understanding the geometry of more general abelian varieties as well. Our second and primary objective is to take this opportunity to elaborate on motivations underlining the proposed solution of the Riemann-Schottky problem, to introduce a certain circle of ideas and methods, developed in the theory of soliton equations, and to convince the reader that they are algebro-geometric in nature, simple and universal enough to be included in the Handbook of moduli.
In this article we prove in a new way that a generic polynomial vector field in ℂ² possesses countably many homologically independent limit cycles. The new proof needs no estimates on integrals, provides thinner exceptional set for quadratic vector fields, and provides limit cycles that stay in a bounded domain.
Моделирование использования солнечного ветра для орбитальных маневров космического аппарата
Чумаченко Е. Н., Малашкин А. В., Федоренко А. Н. Вестник Воронежского государственного технического университета. 2011. Т. 7. № 11.2. С. 71-75.
Спектральный анализ термоволновых колебаний в слоистых системах
Бондаренко Г. Г., Кокин М. А., Пятых Д. С. и др. Перспективные материалы. 2011. № 5. С. 91-95.
A method based on the spectral analysis of thermowave oscillations formed under the effect of radiation of lasers operated in a periodic pulsed mode is developed for investigating the state of the interface of multilayered systems. The method is based on high sensitivity of the shape of the oscillating component of the pyrometric signal to adhesion characteristics of the phase interface. The shape of the signal is quantitatively estimated using the correlation coefficient (for a film–interface system) and the transfer function (for multilayered specimens).
Компьютерное моделирование проникновения криобота под ледяной покров Европы
Чумаченко Е. Н., Данхэм Д. У., Назиров Р. Р. и др. Вестник Нижегородского университета им. Н.И. Лобачевского. 2011. № 6 (1). С. 205-213.
Физика для вузов. Механика и молекулярная физика
Никеров В. А. М.: Издательско-торговая корпорация «Дашков и Ко», 2011.
According to a recent paper \cite{bopt13}, polynomials from the closure $\ol{\phd}_3$ of the {\em Principal Hyperbolic Domain} ${\rm PHD}_3$ of the cubic connectedness locus have a few specific properties. The family $\cu$ of all polynomials with these properties is called the \emph{Main Cubioid}. In this paper we describe the set $\cu^c$ of laminations which can be associated to polynomials from $\cu$.
Kinetical processes in the non- equilibrium nitrogen-oxygen plasma//
Kostinskiy A., Matveev A., Silakov V. Preprint IOFAN. PL. Gen. Phys. Insth, 1990. No. 87.
Kinetical processes in the non- equilibrium nitrogen-oxygen plasma
Instantons beyond topological theory II
Frenkel E., Losev A. S., Nekrasov N. arxiv.org. math. Cornell University, 2008
Conjugacy classes in discrete Heisenberg groups
Roman Budylin. arxiv.org. math. Cornell University, 2014
We study some extension of a discrete Heisenberg group coming from the theory of loop-groups and find invariants of conjugacy classes in this group. In some cases including the case of the integer Heisenberg group we make these invariants more explicit.