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Elliptic solutions to integrable nonlinear equations and many-body systems
Journal of Geometry and Physics. 2019. Vol. 146. No. 103506.
We review elliptic solutions to integrable nonlinear partial differential and difference equations (KP, mKP, BKP, Toda) and derive equations of motion for poles of the solutions. The pole dynamics is given by an integrable many-body system (Calogero-Moser, Ruijsenaars-Schneider). The basic tool is the auxiliary linear problems for the wave function which yield equations of motion together with their Lax representation. We also discuss integrals of motion and properties of the spectral curves.
Priority areas:
mathematics
Language:
English
Flamarion M. V., Pelinovsky E., Wave Motion 2027 Vol. 148 Article 103867
We consider the interaction of two solitary waves in the modified Benjamin–Bona–Mahony
(mBBM) equation in a regime where a small parameter measures the departure from the classical
modified Korteweg–de Vries (mKdV) equation. A regular perturbation method is used to
analyze the modification of the two-soliton wave field induced by the weak non-integrability of
the mBBM equation. We show that, ...
Added: October 23, 2026
Budkov Y., Kalikin N., Journal of Chemical Physics 2026 Vol. 165 No. 16 Article 164108
We derive the local pressure tensor generated by the original Rosenfeld fundamental measure theory (FMT) for hard-sphere fluids from an arbitrary infinitesimal deformation. The variation of a finite-distance FMT kernel is written via the line integrals of the local deformation gradient along the straight segment connecting its end points. The resulting symmetric pressure tensor consists ...
Added: October 22, 2026
Ивченко В. С., Иевлева В. А., Matienko D. et al., Журнал технической физики 2026 № 9 С. 1738–1749
Задача о возбуждении бегущих фонон-поляритонных волн на поверхности полярного кристалла падающей извне световой волной (с частотой, близкой к частоте решеточных колебаний) решена теоретически только для бесконечной открытой поверхности кристалла. В случаях, когда часть поверхности покрыта металлической маской, препятствующей проникновению возбуждающего излучения к атомам среды, и эта маска имеет произвольную форму, общепризнанного решения неоднородной задачи нет. ...
Added: October 20, 2026
Logvenkov S. A., Известия РАН. Механика жидкости и газа 2026 № 3 С. 59–75
The problem of the evolution of cell volume fraction in a spherical aggregate composed of cells,
extracellular matrix, and fluid is considered. The aggregate is surrounded by extracellular matrix. The
problem formulation employs a multiphase model of a biological continuum, previously developed by the
author, consisting of two actively interacting solid phases and a fluid. The propagation of ...
Added: October 20, 2026
Lavrukhina E. A., Krasavin D. P., Krishtopenko S. S. et al., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 No. 22 Article 225414
We study coherent electric manipulation of magnetic field induced localized states at a double kink of a helical edge in a HgTe/CdHgTe quantum well. An in-plane magnetic field opens a gap in the one-dimensional (1D) edge spectrum, while changes in the edge orientation generate localized in-gap states at the kinks. We show that, for suitable ...
Added: October 19, 2026
Lev Pyatko, Sergey Aksenov, Regular and Chaotic Dynamics 2026 Vol. 31 No. 5 P. 794–813
In the circular restricted three-body problem, families of periodic and quasi-periodic orbits exist in the vicinity of the libration points and are of significant interest for practical applications. This work presents a neural network-based algorithm for orbit construction and station-keeping, applicable to both periodic and quasi-periodic orbits near collinear libration points. The method employs a ...
Added: October 19, 2026
Vorontsova T., М.: Академия, 2025.
The textbook has been prepared in accordance with the requirements of the federal state educational standards for secondary vocational education and is intended for studying the professional modules “Information Security in Information and Telecommunication Systems and Networks Using Software and Hardware‑Software Tools, Including Cryptographic Protection Tools” and “Information Security in Automated Systems Using Software and ...
Added: October 19, 2026
Смерчанский П. С., Koledov V. V., Kamantsev A. P. et al., Physics of Metals and Metallography 2026 Vol. 127 No. 6-7 P. 689–693
Heusler alloys of the Ni2MnX family, where X = Ga, In, Sn, …, which have been shown to exhibit
giant magnetocaloric effect (MCE) and magnetically controlled shape memory effect due to thermoelastic
magnetostructural phase transition (MSPT), continue to attract attention. However, these functional properties are fully manifested in strong magnetic fields of at least several T. Currently, ...
Added: October 19, 2026
Naumov A., Рубцов А. С., Samsonov S. et al., Успехи математических наук 2026 Т. 81 № 4 (490) С. 161–162
Краткое сообщение рассматривает Моментные оценки для стохастической аппроксимации ...
Added: October 17, 2026
Roman Avdeev, Yulia Zaitseva, Mediterranean Journal of Mathematics 2026 Vol. 23 No. 7 Article 224
We provide an infinite series of commutative finite-dimensional Gorenstein local algebras A_n for n ≥ 2. We give an elementary proof that the maximal ideal of every algebra A_n possesses a one-dimensional subspace that is different from the socle and invariant under the automorphism group of A_n. The latter implies that the algebras A_n fail ...
Added: October 17, 2026
Gordin V. A., Efremenko D., Boundary-Layer Meteorology 2026 Vol. 192 No. 51
An inverse problem of reconstructing the turbulent exchange tensor from large archives of observed wind profiles within the Åkerblom–Ekman (A-E) model framework is investigated using high-vertical-resolution radiosonde observations. The reconstructed tensor provides improved agreement between modeled and observed wind profiles compared to classical formulations based on real turbulent exchange coefficient. Instead of the classical A-E ...
Added: October 16, 2026
Kuznetsov A. P., Sedova Y. V., Stankevich N., Chaos, Solitons and Fractals 2026 Vol. 213 No. 12 Article 119309
We analyze the interaction of a quasi-periodic subsystem, in which two-, three-, and four- frequency quasi-periodic oscillations are possible, with a chaotic subsystem. A discrete version is obtained via the Euler scheme from the corresponding flow model. The dynamics of individual subsystems are discussed, including quasi-periodic bifurcations of invariant tori and the occur rence of ...
Added: October 16, 2026
Aleksei Samarin, Nazarenko A., Nazarenko D. et al., Machine Learning and Knowledge Extraction 2026 Vol. 8 No. 10 Article 330
Automated microscopic image analysis is essential for quantitative microbiology, yet manual acquisition and generic recognition models struggle with morphological variability and scene artifacts. We address both ends of this pipeline. First, we present a low-cost, open-source acquisition system, based on an Arduino UNO R3 microcontroller and NEMA 17 stepper motors, that automates focusing, magnification, and ...
Added: October 14, 2026
Тукачев Н. В., Bataev V., Abramenkov A. et al., Computational and Theoretical Chemistry 2016 No. 1080 P. 23–32
Electronic state calculations, such as equilibrium geometry parameters, harmonic vibrational frequencies and potential barriers to conformational transitions (as well as conformer energy differences in excited states), using ab initio methods, such as MP2, CCSD(T), CASSCF, CASPT2 and MRCI, were carried out on the formamide molecule in the ground (S0) and the lowest excited singlet (S1) ...
Added: October 14, 2026
Тукачев Н. В., Bataev V. А., Godunov I. А., Journal of Quantitative Spectroscopy and Radiative Transfer 2016 Vol. 177 P. 291–300
For conformers of the N-methylformamide (HCONHCH3) molecule, calculations of equilibrium geometry parameters, harmonic vibration frequencies, energy differences and potential barriers to conformational transitions were performed in the ground (S0) and lowest excited singlet (S1) and triplet (T1) electronic states. In the S0 state, the molecule exists in trans and cis stable conformations (having Cs symmetry). ...
Added: October 14, 2026
Тукачев Н. В., Bataev V. А., Godunov I. А., Journal of Quantitative Spectroscopy and Radiative Transfer 2017 Vol. 192 P. 30–41
For acetamide molecule (CH3CONH2) in the ground (S0) and lowest excited singlet (S1) and triplet (T1) electronic states calculations of equilibrium geometry parameters, harmonic vibrational frequencies and barriers to conformational transitions (also conformer energy differences in excited states) using following ab initio methods: MP2, CCSD(T), CASSCF, CASPT2 and MRCI were performed. One-, two- and three-dimensional ...
Added: October 14, 2026
Тукачев Н. В., Bataev V. A., Godunov I. A., Computational and Theoretical Chemistry 2017 Vol. 1113 P. 82–93
Equilibrium geometry parameters, harmonic vibrational frequencies and barriers to conformational transitions and conformer energy differences for N-methylacetamide (CH3CONHCH3) molecule in S0, S1 and T1 electronic states were calculated in MP2 (S0) and CASPT2 (S1, T1) levels of theory. It is known that there are two planar (or effectively planar) conformers of N-methylacetamide in the ground ...
Added: October 14, 2026
Тукачев Н. В., Maslennikov D., Sosorev A. et al., The Journal of Physical Chemistry Letters 2019 Vol. 10 No. 12 P. 3232–3239
Conformational space of polyphenylenevinylene oligomers is systematically investigated computationally at energies relevant for room temperature dynamics in a solvent and in a solid state. Our calculations show that optimal oligomer structures are essentially planar. However, lack of a deep minimum at the planar geometry allows for large molecular deformations even at very low temperatures. At ...
Added: October 14, 2026
Levashev V., / Series arXiv "math". 2026. No. 2609.06010.
We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...
Added: September 24, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
By analyzing the ...
Added: September 24, 2026
Medvedev V., / Series arXiv "math". 2026.
We study complete static manifolds with boundary admitting a nowhere-vanishing static potential. Our main result shows that, under a natural lower bound relating the scalar curvature and the boundary mean curvature, a simple static manifold with boundary must in fact have positive scalar curvature, negative boundary mean curvature, and be compact; we also obtain explicit ...
Added: September 19, 2026
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026