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Equations for deep water counter streaming waves and new integrals of motion
Fluids. 2019. Vol. 4. No. 1. Article 47.
Dyachenko A.
The waves on a free surface of 2D deep water can be split into two groups: the waves moving to the right, and the waves moving to the left. A specific feature of the four-wave interactions of water waves allows to describe the evolution of the two groups as a system of two equations. The fundamental consequence of this decomposition is the conservation of the “number of waves” in each particular group. The envelope approximation for the waves in each group of counter streaming waves is obtained.
Dmitriev A., Kornilov V., Batienkov R., Lecture Notes in Civil Engineering 2026 Vol. 886 P. 249–255
Numerous studies have provided compelling evidence that the probability distribution of avalanche sizes follows a power law, and that 1/f noise is present in the stochastic dynamics of landslides. We present a theoretical explanation of these phenomena within the framework of self-organized criticality theory, proposing a discrete-time model in the form of a sandpile cellular ...
Added: October 13, 2026
Dmitriev A., Shulman I., Lebedev A., Studies in Computational Intelligence 2026 Vol. 1265 P. 266–273
A discrete-time model is presented for the self-organization of the X/Twitter social network to the edge of a phase transition, characterized by avalanche-like propagation of information in the network. The model is based on the analogy between the critical dynamics of the X social network and sandpile cellular automata with Manna rule on the Chung-Lu ...
Added: October 13, 2026
Arutyunov K., Kharitonov I. A., Petrosyants K. O., JETP Letters 2026 Vol. 124 No. 6 P. 1–16
Superconducting properties of metallic micro- and nanowires can be entirely different from those of bulk superconductors. Of particular interest is the nonequilibrium current-induced state of a quasi-one-dimensional superconducting channel. The most interesting phenomenon here is the stepped I–V characteristic, explained by a process known as phase slip center activation. If the origin of such step-like ...
Added: October 13, 2026
Makarov D. M., Kalikin N., Fashchevsky K. A. et al., Electrochimica Acta 2026 Vol. 579 Article 150159
Machine learning (ML) has become a powerful tool for accelerating the development of carbon-based supercapacitors;
however, most published models assume that a single predictive framework can describe both conventional
porous carbons and hybrid carbon electrodes. Here, we test this assumption using a comprehensive
benchmark dataset and an extended literature-curated dataset enriched with synthesis- and electrolyte-related
descriptors. Three ML algorithms ...
Added: October 13, 2026
Батова О. Н., Савинецкая Л. Е., Проявка С. В. et al., Nature Conservation Research. Заповедная наука 2026 Т. 11 № 4 С. 25–39
Spermophilus suslicus is a threatened species listed in Red Data Books at all levels (from regional Red Data
Books to the IUCN Red List of Threatened Species), and it currently requires special conservation activity.
Over the past 30–50 years, its range has changed from continuous to mosaic, and its population has declined
everywhere. In 2015, in Russia experimental ...
Added: October 13, 2026
Махлуф М., Ozhegov R., Elezov M. et al., Фотоника 2026 Vol. 20 No. 6 P. 414–423
This paper compares the ranging precision of direct time-of-flight (dToF) and non-line-of-sight (NLOS) LiDAR architectures, both using a superconducting nanowire single-photon detector (SNSPD). Both systems operate at 1550 nm with a 50 ps pulsed laser and time-correlated single-photon counting (TCSPC). The dToF configuration achieved approximately 100 µm precision at 10 m, while the NLOS configuration achieved 500 µm precision for ...
Added: October 12, 2026
Mishuris G., Meylan M. H., Pelinovsky E., Journal of Fluid Mechanics 2026 Vol. 1045 Article A4
In this paper, we revisit the classic problem of a wave field on a sloping beach of an arbitrary angle and propose a general approach that allows the computation of regular solutions of the problem regardless of the angle. We use the Mellin-transform technique, reducing the problem to singular integral equations with fixed-point singularities of ...
Added: October 12, 2026
Singapore: Springer, 2026.
This volume presents the Proceedings of the 34th IUPAP Conference on Computational Physics (CCP2023), held in Kobe, Japan on August 4–8, 2023. It offers a collection of peer-reviewed articles that highlight recent developments in computational and simulation research across various areas of physics. Key topics include the use of data science, quantum computing, and machine ...
Added: October 12, 2026
Ari G., Liu X., Jiang L. et al., Ecological Indicators 2026 Vol. 191 Article 115592
Snow drought has become a research hotspot due to its widespread impacts on ecosystems and water resources, yet its effects on vegetation phenology remain relatively understudied. Focusing on the Mongolian Plateau, this study used the Snow Water Equivalent Index and the start of growing season (SOS) to assess the associations between snow drought and vegetation ...
Added: October 12, 2026
He Y., Slunyaev A., Mori N. et al., Physica D: Nonlinear Phenomena 2026 Vol. 488 Article 135098
Extreme wave localizations in nonlinear dispersive media, arising from modulation instability in weakly nonlinear
wave interactions, can be effectively modeled by breather solutions. These breathers are exact solutions
of the nonlinear Schrödinger equation and provide accurate models for understanding and controlling unidirectional
rogue wave dynamics in numerical simulations or laboratory settings. A recent study by Y. He et ...
Added: February 12, 2026
Slunyaev A., Фундаментальная и прикладная гидрофизика 2025 Т. 18 № 4 С. 28–49
Regimes and limitations of the numerical solution method for hydrodynamic equations using the approximation of the near-surface velocity potential by the high-order Taylor expansion (High Order Spectral Method, HOSM) are investigated. This approach is considered in the context of simulation of large ensembles of sea surface displacement fields under finite-depth conditions. The main attention is ...
Added: February 12, 2026
Delitsyn A., Konyaev D., Vasiliy Kakurin et al., Communications in Nonlinear Science and Numerical Simulation 2026 Vol. 153 Article 109492
This paper presents an enhanced perturbation theory-based approach for compensating nonlinear distortion in long-haul fibre-optic communication systems. The proposed method combines perturbation-based compensator for fibre nonlinearity with machine learning, achieving high compensation accuracy with reduced computational complexity. We derive the theoretical framework for a modified perturbation method that leverages an effective lossless fibre model, uses ...
Added: November 11, 2025
Meshcheryakov A. A., A.R. Safin, Kalyabin D. et al., Physics of the Solid State 2025 Vol. 67 No. 1 P. 72–77
The phenomenon of mode hybridization in the exchange-coupled two-layer antiferromagnet|ferromagnet structure has been theoretically investigated. Expressions describing the dependence of the resonant frequencies of magnetization oscillations on the external magnetic field have been obtained by the method of Hamiltonian formalism. The effect of the coupling strength between the ferro- and antiferromagnetic layers on the width ...
Added: July 2, 2025
Abrashkin A. A., World Scientific Publishing Co. Pte. Ltd, 2025.
This book is devoted to the problems of the analytical description of incompressible fluid flows in Lagrangian variables. Commonly, specialists in fluid dynamics prefer to use the Euler approach. For example, even classical textbooks by J. Batchelor, L.G. Loitsyansky, L.D. Landau, and E.M. Lifshitz do not provide the Lagrange equations of f luid dynamics. Exceptions ...
Added: January 28, 2025
Zabrodin A., Успехи математических наук 2023 Т. 78 № 2(470) С. 149–188
We find integrals of motion for the recently introduced
deformed Ruijsenaars–Schneider many-body system, which is the dynamical system for poles of elliptic solutions to the Toda lattice with constraint
of type B. Our method is based on the fact that the equations of motion
for this system coincide with those for pairs of Ruijsenaars–Schneider particles which stick together ...
Added: December 1, 2023
Dyachenko A., Kachulin D., Zakharov V., Lobachevskii Journal of Mathematics 2017 Vol. 38 No. 5 P. 888–892
Presented are the results of experiments on calculation of Probability Distribution Functions for elevations of waters waves in numerical tank. Statistics of waves of anomalous amplitude, or freak-waves were compared both for nonlinear and linear models. Obviously, linear model demonstrates the exact Rayleigh distribution of surface elevations while PDFs for nonlinear equation have tails (for ...
Added: October 22, 2022
Dyachenko A., Kachulin D., Zakharov V., Journal of Ocean Engineering and Marine Energy 2017 Vol. 3 No. 4 P. 409–415
Water waves have long been a subject of attention of both mathematicians and physicists. The formulation of the problem is simple enough to be considered fundamental, but as of yet many questions still remain unanswered and many phenomena associated with wind-driven turbulence remain puzzling. We consider a “unidirectional” motion of weakly nonlinear gravity waves, i.e., ...
Added: October 22, 2022
Dremov S., Kachulin D., Dyachenko A., Fluids 2022 Vol. 7 No. 6 Article 204
In this paper we propose two Hamiltonian models to describe two-dimensional deep water waves propagating on the surface of an ideal incompressible three-dimensional fluid. The idea is based on taking advantage of the Zakharov equation for one-dimensional waves which can be written in the form of so-called compact equations. We generalize these equations to the ...
Added: October 22, 2022
Dyachenko A., Studies in Applied Mathematics 2020 Vol. 144 No. 4 P. 493–503
One of the essential tasks of the theory of water waves is a construction of simplified mathematical models, which are applied to the description of complex events, such as wave breaking, appearing of freak waves in the assumption of weak nonlinearity. The Zakharov equation and its simplification, such as nonlinear Schrodinger equations and Dysthe equations, ...
Added: October 21, 2022
A. A. Abrashkin, Monatshefte fur Mathematik 2022 Vol. 199 No. 4 P. 717–732
Propagation of periodic stationaryweakly vortical gravitationalwaves on the freewater surface is considered. Similar wave motion was studied by Gouyon (Ann de la Fac des Sci de l’Université de Toulouse Sér 4(22):1–55, 1958) in linear and quadratic approximations in small parameter of the wave’s steepness ε for the deep water conditions.
In this paper this result is considered for the ...
Added: October 13, 2022
Feigin B. L., Mukhin E., Jimbo M., Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 2022 Vol. 18 Article 51
We introduce an algebra Kn which has a structure of a left comodule over the quantum toroidal algebra of type An−1. Algebra Kn is a higher rank generalization of K1, which provides a uniform description of deformed W algebras associated with Lie (super)al-gebras of types BCD. We show that Kn possesses a family of commutative subalgebras. © 2022, ...
Added: August 17, 2022
Abrashkin A. A., Pelinovsky E., Journal of Physics A: Mathematical and Theoretical 2021 Vol. 54 No. 39 Article 395701
To study stationary periodic weakly vortical waves on water (the Gouyon waves), the method of the modified Lagrangian variables is suggested. The wave vorticity Ω is specified as a series in the small steepness parameter ε in
the form: Ω =\sum( ε^n · Ω_n (b)), where Ω_n are arbitrary functions of the vertical Lagrangian coordinate b. Earlier Gouyon (1958) studied ...
Added: October 5, 2021
Ivanov S. K., Kamchatnov A.M., Physics of Fluids 2019 Vol. 31 Article 057102
We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated, and motion of the dispersive shock edges is studied within the Whitham theory of modulations. Simple analytical formulas are obtained for asymptotic stage ...
Added: February 4, 2021
Feigin B. L., Jimbo M., Mukhin E., Journal of Physics A: Mathematical and Theoretical 2017 Vol. 50 No. 46 Article 464001
We identify the Taylor coefficients of the transfer matrices corresponding to quantum toroidal algebras with the elliptic local and non-local integrals of motion introduced by Kojima, Shiraishi, Watanabe, and one of the authors.
That allows us to prove the Litvinov conjectures on the Intermediate Long Wave model.
We also discuss the (gl(m),gl(n)) duality of XXZ models in ...
Added: November 5, 2020