?
Properties of synchronous collisions of solitons in the Korteweg–de Vries equation
Communications in Nonlinear Science and Numerical Simulation. 2023. Vol. 118. Article 107048.
Tatiana V. Tarasova, Alexey V. Slunyaev
Synchronous collisions of solitons of the Korteweg–de Vries equation are considered as a representative example of the interaction of a large number of solitons in a soliton gas. Statistical properties of the soliton field are examined for a model distribution of soliton amplitudes according to a power law. N-soliton solutions (N ≤ 50) are constructed
with the help of a numerical procedure using the Darboux transformation and 100-digits arithmetic. It is shown that there exist qualitatively different patterns of evolving multisoliton solutions depending on the amplitude distribution. Collisions of a large number of solitons lead to the decrease of values of statistical moments (the orders from
3 to 7 have been considered). The statistical moments are shown to exhibit long intervals of quasi-stationary behavior in the case of a sufficiently large number of interacting solitons with close amplitudes. These intervals can be characterized by the maximum value of the soliton gas density and by ‘‘smoothing’’ of the wave fields in integral sense. The analytical estimates describing these degenerate states of interacting solitons are obtained.
Keywords: уравнение Кортевега - де Вризаstatistical momentsSoliton interactionKorteweg - de Vries equationвзаимодействие солитоновСТАТИСТИЧЕСКИЕ МОМЕНТЫ
Publication based on the results of:
П.А.Беспалов, О.Н. Савина, Геомагнетизм и аэрономия 2025 Т. 65 № 5 С. 620–628
Several basic models of frequency dynamics in quasi-periodic VLF emissions with spectral form repetition
periods from 10 to 300 s are considered. In all cases, we are talking about manifestations of cyclotron instability
of electron radiation belts thet are well described within the framework of the plasma magnetospheric maser
theory based an the averaged self-consistent system of quasi-linear ...
Added: April 25, 2026
Bondarenko G.G., Fisher M. R., Kristya V. I., Bulletin of the Russian Academy of Sciences: Physics 2026 Vol. 90 No. 4 P. 572–576
A model of the cathode layer of a glow gas discharge with a thin dielectric film on a fraction of the
cathode’s working surface is formulated. It is shown that a glow discharge most rapidly transits to an arc discharge,
accompanied by a significant increase in discharge current density and a decrease in cathode voltage
drop, if the ...
Added: April 25, 2026
Pochinka O., Yakovlev E., Shmukler V., Russian Journal of Nonlinear Dynamics 2026
Every discrete dynamical system (cascade) generated by a homeomorphism induces a continuous
dynamic system (flow) — a suspension. However, not every flow is equivalent to a suspension
over a cascade, a necessary and sufficient condition for this is the existence of a global
section for the flow. In the case of the existence, the flow is equivalent to ...
Added: April 24, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Selecta Mathematica, New Series 2026 Vol. 32 Article 25
We revise the notion of the blobbed topological recursion by extending it to the setting of generalized topological recursion as well as allowing blobs which do not necessarily admit topological expansion. We show that the so-called non-perturbative differentials form a special case of this revisited version of blobbed topological recursion. Furthermore, we prove the KP ...
Added: April 23, 2026
Kazaryan M., Lando S., Kodaneva N., Journal of Geometry and Physics 2026 No. 225 Article 105841
Weight systems associated to the Lie algebras 𝔤𝔩(N) for N = 1,2,... can be unified into auniversal one. The construction is based on an extension of the 𝔤𝔩(N) weight systems to permutations. This universal weight system takes values in the algebra of polynomials C[N;C1,C2,...] in infinitely many variables. We show that under the substitution Cm ...
Added: April 23, 2026
Kychkin A., Chernitsin I., Прикладная информатика 2026 Т. 21 № 1 С. 40–58
The results of the development of a software microservice embedded in atmospheric air quality monitoring systems to support the identification of industrial pollution sources are presented. The emission and subsequent spread of harmful substances in the lower layers of the atmosphere is dynamic and characterized by high uncertainty due to the specific features of technological ...
Added: April 23, 2026
Zadkov V., Plasmonics 2026 Vol. 21 P. 1503–1512
Plasmonic nanostructures typically exhibit shifts in their resonant wavelength in response to changes in the refractive index of the surrounding medium. This limits their applications in scenarios requiring stable optical resonances. Here we present a metallic-dielectric hybrid metasurface that exhibits stable multi-wavelength resonance even if the refractive index of its surrounding varies. To quantitatively evaluate the stability of ...
Added: April 22, 2026
IEEE, 2026.
Added: April 21, 2026
Galkin O., Galkina S., Ястребова И. Ю., Журнал Средневолжского математического общества 2026 Т. 28 № №1 С. 11–30
Polynomials of least deviation from zero play an important role in the theory and practice of numerical methods. They can be used to solve problems of optimizing the properties of various computational algorithms. Our work is devoted to the study of polynomials of least deviation from zero on a ray in the exponential norm. In ...
Added: April 20, 2026
Shchur L., Antonov D., Burovski E., International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2026 P. 2650132-1–2650132-9
We present a simple model that simulates the possible influence of one society on another. Specifically, two societies evolve deterministically according to the well-known Nowak-May spatial game with the addition of mutual influence through connections that reflect the current states of the societies. This may be related to the influence of a global information resource ...
Added: April 20, 2026
Qin X., Deng Y., Shchur L. et al., / Series arXiv "math". 2026. No. 2603.02962.
We perform a Monte Carlo analysis of the Ising model on many three-dimensional lattices. By means of finite-size scaling we obtain the critical points and determine the scaling dimensions. As expected, the critical exponents agree with the three-dimensional Ising universality class for all models. The irrelevant field, as revealed by the correction-to-scaling amplitudes, appears to ...
Added: April 20, 2026
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
Added: April 20, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Kalikin N., Брандышев П. Е., Budkov Y., Journal of Chemical Physics 2026 Vol. 164 Article 154904
This study presents a mean-field theory for zwitterionic polymer solutions confined within attractive slit-like nanopores. Building upon our prior model for self-coacervation [Budkov et al., Soft Matter 19, 3281–3289 (2023)], we demonstrate that strong electrostatic dipole–dipole correlations between monomeric units, coupled with attraction to pore walls, can induce capillary-driven liquid–liquid phase separation inside the pore—a ...
Added: April 18, 2026
Moiseev E., Масютин Д. А., Мельниченко И. А. et al., Optics and Laser Technology 2025 Vol. 201 No. 115289 P. 1–5
Lasing at a wavelength near 255 nm is demonstrated in AlGaN whispering gallery mode microlasers with radii ranging from 1 to 3 µm fabricated on sapphire substrates, representing one of the shortest-wavelength realizations of microdisk lasers on this technologically relevant platform. The minimum threshold energy was 8.8 pJ (power density ≈ 280 kW/cm2) for a microlaser with a ...
Added: April 18, 2026
Petrov I., Doklady Mathematics 2026 Vol. Volume 112 P. S103–S110
This paper examines games on networks with linear best responses, which allow for the analysis of how interaction structures influence agents’ strategic behavior. Special attention is given to intervention issues in such models, particularly in selecting optimal intervention strategies aimed at maximizing the central planner’s objective function. Two main control policies are analyzed: individual agent ...
Added: April 17, 2026
Didenkulova E., Flamarion M., Pelinovsky E., Physica D: Nonlinear Phenomena 2025 Vol. 481 Article 134815
A comparison of the statistical characteristics of a rarefied soliton gas is carried out within the framework of integrable and non-integrable equations from the Korteweg-de Vries (KdV) hierarchy. As examples, multi-soliton solutions of the modified KdV equation, and the modular Schamel equation are considered. A common property of the dynamics of bipolar solitons is the ...
Added: March 11, 2026
Flamarion M. V., E. Pelinovsky, E. Didenkulova, Physics of Wave Phenomena 2025 Vol. 33 No. 1 P. 9–19
The present paper is devoted to the study of the dynamics of narrowband wave fields within the
nonintegrable Schamel equation, which plays an important role in plasma physics, wave dynamics in metamaterials,
and electrical circuits. A Monte Carlo approach is used to obtain a large number of random independent
realizations of the wave fields, allowing for an investigation ...
Added: March 23, 2025
Flamarion M. V., Pelinovsky E., Russian Journal of Mathematical Physics 2024 Vol. 31 No. 2 P. 199–208
The vortical Whitham equation is modeled with quadratic and cubic nonlinearity, satisfying the unidirectional dispersion relation used to describe the propagation of nonlinear waves in the presence of a vertically sheared current of constant vorticity. In this article, we neglect the quadratic nonlinearity to numerically investigate solitary wave interactions. We show that the geometric Lax ...
Added: June 30, 2024
Pelinovsky E., Talipova T., Didenkulova E., Physics Letters A 2024 Vol. 507 Article 129489
The dynamics of waves of sign-variable shape has been studied within the framework of the Hopf equation (ut +Fux = 0) with a non-analytic propagation velocity containing the modulus of the function at the zero crossing (F ~ |u|α). It is shown that Riemann waves exist only for a certain smoothness of the function F[u(x)] ...
Added: May 30, 2024
Flamarion M., Pelinovsky E., Didenkulova E., Chaos, Solitons and Fractals 2024 Vol. 180 Article 114495
Soliton gas or soliton turbulence is a subject of intense studies due to its great importance to optics, hydrodynamics, electricity, chemistry, biology and plasma physics. Usually, this term is used for integrable models where solitons interact elastically. However, soliton turbulence can also be a part of non-integrable dynamics, where long-lasting solutions in the form of ...
Added: March 15, 2024
A. V. Slunyaev, Kokorina A. V., E. N. Pelinovsky, Communications in Nonlinear Science and Numerical Simulation 2023 Vol. 127 Article 107527
Effects of nonlinear dynamics of solitary waves and wave modulations within the
modular (also known as quadratically cubic) Korteweg–de Vries equation are studied
analytically and numerically. Large wave events can occur in the course of interaction
between solitons of different signs. Stable and unstable (finite-time-lived) breathers can
be generated in inelastic collisions of solitons and from perturbations of two ...
Added: December 20, 2023
Ekaterina Didenkulova, Pelinovsky E., Flamarion M., Mathematics 2023 Vol. 11 No. 22 Article 4649
Pair soliton interactions play a significant role in the dynamics of soliton turbulence. The interaction of solitons with different polarities is particularly crucial in the context of abnormally large wave formation, often referred to as freak or rogue waves, as these interactions result in an increase in the maximum wave field. In this article, we ...
Added: December 11, 2023
Didenkulova E., Талипова Т. Г., Диденкулов О. И., Экологические системы и приборы 2022 № 12 С. 55–64
The article presents the results of numerical simulation of the dynamics of solitary internal waves’ ensembles in a stratified (vertically inhomogeneous) ocean for hydrophysical conditions close to those on the Indian Ocean shelf. Ensembles of unipolar and bipolar solitons, as well as solitons and breathers with random amplitudes and phases are considerate. Estimates of the statistical characteristics of ...
Added: January 31, 2023