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## On factorized Lax pairs for classical many-body integrable systems

Reviews in Mathematical Physics. 2019. Vol. 31. No. 06. P. 1–42.

Васильев М. А., Zotov A.

In press

In this paper we study factorization formulae for the Lax matrices of the classical Ruijsenaars-Schneider and Calogero-Moser models. We review the already known results and discuss their possible origins. The first origin comes from the IRF-Vertex relations and the properties of the intertwining matrices. The second origin is based on the Schlesinger transformations generated by modifications of underlying vector bundles. We show that both approaches provide explicit formulae for M-matrices of the integrable systems in terms of the intertwining matrices (and/or modification matrices). In the end we discuss the Calogero-Moser models related to classical root systems. The factorization formulae are proposed for a number of special cases.

Окубо Ю. undefined., Journal of Physics: Conference Series 2017 Vol. 804 No. 012036 P. 1–8

We investigate the existence and the orthogonality of the generalized Jack symmetric functions which play an important role in the AGT relations. We show their orthogonality by deforming them to the generalized Macdonald symmetric functions. ...

Added: October 26, 2017

A. V. Slunyaev, T. V. Tarasova, Chaos 2022 Vol. 32 Article 101102

Synchronous collisions between a large number of solitons are considered in the context of a statistical description. It is shown that, during the interaction of solitons of the same signs, the wave field is effectively smoothed out. When the number of solitons increases and the sequence of their amplitudes decay slower, the focused wave becomes even smoother ...

Added: October 14, 2022

Zhuzhoma E. V., Medvedev V., Исаенкова Н. В., Нелинейная динамика 2017 Т. 13 № 3 С. 399–412

В статье, используя методы теории динамических систем Морса–Смейла, авторы рассматривают топологическую структуру для точечно-зарядной модели магнитного поля областей фотосферы. Для произвольного количества зарядов (безотносительно к их местоположению) и не предполагая потенциальности поля <span data-mathml="B⃗ (следовательно, не используя конкретных формул), авторы приводят оценки, связывающие количества зарядов определенного типа с количеством нуль-точек. Для граничных оценок описывается топологическая структура магнитного ...

Added: October 12, 2017

Elena R. Loubenets, Kuznetsov S., Louis Hanotel, Journal of Physics A: Mathematical and Theoretical 2024 Vol. 57 No. 5 Article 055302

For the maximal violation of all Bell inequalities by an arbitrary pure two-qudit state of any dimension, we derive a new lower bound expressed via the concurrence of this pure state. This new lower bound and the upper bound on the maximal Bell violation, found in [J. Phys. A: Math. Theor. 55, 285301 (2022)] and ...

Added: January 6, 2024

Kurkina O. E., Kurkin A. A., Rouvinskaya E. et al., Письма в Журнал экспериментальной и теоретической физики 2012 Т. 95 № 2 С. 98–103

Nonlinear wave dynamics is discussed using the extended modified Korteweg–de Vries equation that includes the combination of the third- and fifth- order terms and is valid for waves in a three-layer fluid with so-called symmetric stratification. The derived equation has solutions in the form of solitary waves of various polarities. At small amplitudes, they are ...

Added: August 24, 2012

Aseeva N., Gromov E., Onosova I. V. et al., JETP Letters 2016 Vol. 103 No. 10 P. 653–657

Evolution of solitons is addressed in the framework of a third-order nonlinear Schrödinger equation (NLSE), including nonlinear dispersion, third-order dispersion and a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a spatial-domain counterpart of the SRS term, which is well known as a part of the temporal domain NLSE in optics. In this context, it is induced by the ...

Added: June 28, 2016

Musaev E., Berman D. S., Thompson D. C., Journal of High Energy Physics 2012 Vol. 1210

The reduction of the duality invariant approach to M-theory by a U-duality group valued
Scherk-Schwarz twist is considered. We show that all gaugings of SUGRA can be obtained
by dimensional reduction of the extended space. ...

Added: October 20, 2014

. IEEE, 2020.

Added: August 19, 2020

Dmitriev A., Kornilov V., Dmitriev V. et al., Frontiers in Physics 2022 Vol. 10 No. 839383 Article 839383

The sandpile cellular automata, despite the simplicity of their basic rules, are adequate mathematical models of real-world systems, primarily open nonlinear systems capable to self-organize into the critical state. Such systems surround us everywhere. Starting from processes at microscopic distances in the human brain and ending with large-scale water flows in the oceans. The detection ...

Added: March 14, 2022

Pelinovsky E., Didenkulova I., Rybkin A., Journal of Fluid Mechanics 2014 Vol. 748 P. 416–432

We present an exact analytical solution of the nonlinear shallow water theory for wave run-up in inclined channels of arbitrary cross-section, which generalizes previous studies on wave run-up for a plane beach and channels of parabolic cross-section. The solution is found using a hodograph-type transform, which extends the well-known Carrier–Greenspan transform for wave run-up on ...

Added: November 19, 2014

Musaev E., Akhmedov E., Gahramanov I., JETP Letters 2011 Vol. 93 No. 9 P. 545–550

The Polchinski equations for the Wilsonian renormalization group in the D-dimensional matrix scalar field theory can be written at large N in a Hamiltonian form. The Hamiltonian defines evolution along one extra holographic dimension (energy scale) and can be found exactly for the subsector of Trϕ n (for all n) operators. We show that at ...

Added: October 20, 2014

Budkov Y., Journal of Physics: Condensed Matter 2019 Vol. 31 P. 078002–078003

We reply to the comment on our paper by Budkov (2018 J. Phys.: Condens. Matter 30 344001). ...

Added: January 4, 2019

. CRC Press, 2016.

In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors ...

Added: October 26, 2021

Elena R. Loubenets, Khrennikov A., Journal of Physics A: Mathematical and Theoretical 2019 Vol. 52 No. 43 P. 435304-1–435304-14

For an even qudit dimension d≥2, we introduce a class of two-qudit states exhibiting perfect correlations/ anticorrelations and prove via the generalized Gell-Mann representation that, for each two-qudit state from this class, the maximal violation of the original Bell inequality is bounded from above by the value 3/2 -- the upper bound attained on some ...

Added: September 26, 2019

Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65–83

We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...

Added: November 1, 2019

Nicol R., Chapman S., Vertes P. et al., Journal of Neurophysiology (США) 2012 Vol. 107 No. 5 P. 1421–1430

How do human brain networks react to dynamic changes in the sensory environment? We measured rapid changes in brain network organization in response to brief, discrete, salient auditory stimuli. We estimated network topology and distance parameters in the immediate central response period, <1 s following auditory presentation of standard tones interspersed with occasional deviant tones ...

Added: October 23, 2014

Семин С. В., Kurkina O. E., Kurkin A. A. et al., Труды НГТУ им. Р.Е. Алексеева 2012 № 2(95) С. 48–65

Purpose: Numerical modeling of internal baroclinic disturbances of different shapes in a model lake with variable depth, analysis of velocity field of wave-induced current, especially in the near-bed layer.
Approach: The study is carried out with the use of numerical full nonlinear nonhydrostatic model for stratified fluid.
Findings: The full nonlinear numerical modeling of internal wave dynamics ...

Added: October 6, 2012

Budkov Y., Kolesnikov A. L., Polymer Science - Series C 2018 Vol. 60 No. Supplement 1 P. 148–159

Theoretical models of the conformational behavior of flexible polymer chains in mixed solvents enunciated in the world literature during the last decade are critically reviewed. Models describing different mechanisms of coil-to-globule transitions in a good solvent induced by cosolvent addition are highlighted. Special attention is given to the analysis of theoretical approaches to describing the ...

Added: November 30, 2018

49606783, Russian Journal of Mathematical Physics 2019 Vol. 26 No. 2 P. 168–173

The parameters of unstable short-living isotopes are studied from
the mathematical point of view. The values of the chemical potential
and activity parameters that determine the neutron halo arising when
the neutron separates from the nucleus of an unstable isotope are
calculated. The analogy between nuclear physics and economics is
considered from the point of view of such parameters as ...

Added: August 25, 2019

Vostrikov A. V., Borisov N., Abrameshin A. E., Качество. Инновации. Образование 2013 № 8 (99) С. 61–65

In work research of numerical stability of earlier reduced scheme of numerical integration of system of the linear ordinary differential equations developed by authors is conducted. The received condition of numerical stability of the reducing scheme proves possibility of use of this scheme in practice. Operability of the reduced scheme was tested on a real ...

Added: September 9, 2013

Elena R. Loubenets, / Cornell University. Series arXiv "quant-ph". 2012. No. 1210.3270.

Added: September 25, 2016

Marshakov A., Миронов А. Д., Морозов А. Ю., Journal of Geometry and Physics 2011 Vol. 61 P. 1203–1222

We present a summary of current knowledge about the AGT relations for conformal blocks with additional insertion of the simplest degenerate operator, and a special choice of the corresponding intermediate dimension, when the conformal blocks satisfy hypergeometric-type differential equations in position of the degenerate operator. A special attention is devoted to representation of conformal block ...

Added: February 28, 2013

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1–16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020

. М.: Издательство математико-механического факультета МГУ, 2009.

В настоящий сборник вошли аннотации докладов участников XVI международной конференции «Ломоносов» по секции «Математика и механика». ...

Added: February 4, 2013