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Soliton interactions with an external forcing: The modified Korteweg–de Vries framework
Chaos, Solitons and Fractals. 2022. Vol. 165. Article 112889.
Flamarion M. V., Pelinovsky E.
The aim of this work is to study asymptotically and numerically the interaction of solitons with an external
forcing with a variable speed using the forced modified Korteweg–de Vries equation (mKdV). We show that the
asymptotic predictions agree well with numerical solutions for forcings with constant speed and linear variable
speed. Regarding forcing with linear variable speed, we find regimes in which the solitons are trapped at the
external forcing and its amplitude increases or decreases in time depending on whether the forcing accelerates
or decelerates.
Kupavskii A., Noskov F., Forum of Mathematics, Sigma 2026 Vol. 14 Article 124
We call a family of $s$ sets $\{F_1, \ldots, F_s\}$ a sunflower with $s$ petals if, for any distinct $i, j \in [s]$, one has $F_i \cap F_j = \cap_{u = 1}^s F_u$. The set $C = \cap_{u = 1}^s F_u$ is called the {\it core} of the sunflower. It is a classical result of ...
Added: October 8, 2026
Ozhegov R., Махлуф М., Goltsman G. et al., Инженерная физика 2026 № 8 С. 27–39
This paper investigates the theoretical limits of object detection within isotropic scattering media using single-photon lidar. Within a simplified model, we derive the fundamental relationship between the maximum attainable detection range and the required photon count per pulse. Two distinct limiting regimes are analyzed: the ballistic photon regime, which maintains high spatial resolution but necessitates ...
Added: October 8, 2026
Didenkulova E., Chugunov V., Didenkulova I., Wave Motion 2026 Vol. 147 Article 103787
This work presents a new analytical solution of the shallow water theory for cylindrical propagation of long tsunami-like waves in the basin of variable depth. Considered model cases are related to tsunami wave propagation from an asteroid fallen into the sea, or from underwater volcanic eruptions. The corresponding bottom geometries represent radially symmetric obstacles such ...
Added: October 8, 2026
Flamarion M., Didenkulova E., Pelinovsky E., Physics Letters A 2026 Vol. 598 Article 132218
In this letter, bipolar solitary wave interactions in the Schamel equation are revisited numerically. Two simulation settings are considered: repeated collisions in a periodic domain, and the interaction of a positive solitary wave with a train of negative polarity solitary waves of equal amplitude. In the first case, when the amplitudes are comparable, the larger ...
Added: October 8, 2026
Flamarion M. V., Pelinovsky E., Chaos, Solitons and Fractals 2026 Vol. 213 No. 2 Article 119245
This article concerns the study of modulational instability in the rotated-modified Gardner–Whitham (rmGW) equation. This model incorporates both quadratic and cubic nonlinearities, similarly to the Gardner equation, while also retaining the fully dispersive character of the Whitham equation together with a large-scale dispersive term analogous to that in the Ostrovsky equation. Using a classical multiple-scale asymptotic expansion, we ...
Added: October 8, 2026
Люксембург А. А., УРСС, 2005.
Изучается возможность автоматизированного построения математических теорий. Рассматривается дедуктивная система, основанная на языке логики предикатов первого порядка, объектами системы являются математические выражения или формулы, которые описывают математические объекты или их свойства. В дедуктивной системе выводятся математические определения и теоремы. Для доказательства теорем используются методы автоматического доказательства. Разработан алгоритм, выводящий часть формул системы. Для решения задачи используется аппарат математической ...
Added: October 7, 2026
Bernardin C., Gonçalves P., Olla S., Mathematical Physics Analysis and Geometry 2024 Vol. 27 No. 7
We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space. ...
Added: October 6, 2026
Bernardin C., Chhaibi R., Najnudel J. et al., Probability Theory and Related Fields 2026 Vol. 195 P. 1823–1875
We study the celebrated Shiryaev-Wonham filter (Wonham, W.M., in J. Soc. Ind. Appl. Math. 347–369, 1964) in its historical setup, where the hidden Markov jump process has two states. We are interested in the weak noise regime for the observation equation. Interestingly, this becomes a strong noise regime for the filtering equations. Earlier results of ...
Added: October 5, 2026
Ismailov A., Spiridonov V., Успехи математических наук 2026 Т. 81 № 5 С. 183–184
Получена новая формула для цепной дроби Аски–Вильсона в форме отношения двух q-гипер-геометрических рядов. ...
Added: October 5, 2026
Isaev T. F., Шаров А. Н., Журнал вычислительной математики и математической физики 2026 Т. 66 № 1 С. 83–93
Исследуются свойства оптических покрытий на основе использования упрощенного симулятора ошибок в толщинах слоев покрытий при их напылении. Обосновывается возможность такого подхода. Выводятся аналитические оценки среднеквадратичного значения нормы вектора ошибок и степени коррелированности ошибок в толщинах слоев покрытия. Изучается зависимость среднеквадратичного значения нормы вектора ошибок и свойств покрытия от уровня случайных ошибок в слоях. ...
Added: October 5, 2026
Осипова А. М., Пилипенко С. В., Novikov D. I. et al., Physical Review D - Particles, Fields, Gravitation and Cosmology 2026 Vol. 114 Article 063522
We investigate the prospects for observing a specific spectral distortion of the cosmic microwave
background, which occurs due to the anisotropy of the radiation when it is scattered by hot plasma of
galaxy clusters. Detection of this anisotropic Sunyaev-Zel’dovich effect would enable an independent
measurement of the CMB anisotropy multipoles with l 1⁄4 1, 2, 3, allow the ...
Added: October 5, 2026
Abdulkhaev K., Shirokov D., Advances in Applied Clifford Algebras 2026 Vol. 36 P. 1–21
In this paper, we present explicit formulas for the inverse and determinant in geometric (Clifford) algebras over vector spaces of dimension n = 7. The derivation of these formulas is made possible by generalizing the concept of conjugation to basis conjugation operations. We further develop a general method for constructing such formulas over odd-dimensional spaces ...
Added: October 4, 2026
Gribova N. I., Osmanov S. V., Lyashko S. D. et al., Journal of Magnetism and Magnetic Materials 2025 No. 614 P. 1–8
Here we demonstrate nanometer thick iron garnet films with high specific Faraday rotation suitable for
the magneto-optical applications. Bismuth-substituted iron garnet films of compositions Bi1Y2Fe5O12 and
Bi1Tm2Fe5O12 deposited on gadolinium gallium garnet substrate are fabricated and characterized. Their
thicknesses range from 2 to 10 nm, which corresponds to just a few crystal lattice constants. Spectacularly,
Faraday rotation of the ...
Added: October 4, 2026
Kuninets A., IEEE Transactions on Information Theory 2026 P. 1–1
In this work we study the applicability of Quasi-Cyclic Subfield Subcodes of Dual Elliptic (QC-SSDE) codes for integration into code-based cryptographic schemes. Detailed algorithms are provided for constructing parity-check matrices as well as block-circulant parity-check matrices for this family of codes, accompanied by empirical results that enable the construction of QC-SSDE codes with predetermined dimensions. ...
Added: October 3, 2026
Seleznev G., Fominov Yakov V., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 No. 7 Article 074505
Dirty superconducting films with magnetic impurities can exhibit nontrivial behavior in a magnetic field that
polarizes the impurity spins. As predicted by Kharitonov and Feigelman (KF) [JETP Lett. 82, 421 (2005)],
this polarization reduces the exchange scattering rate. Consequently, a parallel magnetic field can enhance
the critical temperature Tc when magnetic-field pair breaking is weak, as realized for ...
Added: October 2, 2026
Zhukov A., Chen F., Zeng Y. et al., Nanoscale 2026 Vol. 18 No. 36 P. 19223–19253
Colloidal semiconductor nanocrystals have emerged as promising materials for next-generation light-emitting diodes (LEDs) owing to their solution processability, tunable emission wavelengths, narrow emission linewidths, and high photoluminescence quantum yields. Among them, anisotropic nanocrystals, including one-dimensional nanorods (NRs) and two-dimensional nanoplatelets (NPLs), offer additional opportunities for controlling transition dipole moment orientation and light out-coupling efficiency. These ...
Added: October 2, 2026
Flamarion M., Pelinovsky E., Chaos, Solitons and Fractals 2026 Vol. 208 No. 3 Article 118271
Two-solitary-wave interactions are investigated within the fourth-order generalized Korteweg–
de Vries equation. This equation is closely related to the classical Korteweg–de Vries equation
but includes a quartic nonlinear term. We show that, although collisions between two solitary
waves are not perfectly elastic, only a small amount of radiation is generated during the
interaction. This allows a clear characterization of ...
Added: March 22, 2026
Kamchatnov A.M., Suleimanov B. I., Tsoy E. N., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2025 Vol. 111 No. 6 Article 064203
In this paper, we derive equations for the dynamics of ring dark solitons in an expanding cloud of a twodimensional Bose-Einstein condensate. Assuming that the soliton’s width is much smaller than its radius, we obtain the Hamilton equations for its evolution. Then they are transformed into the Newton equation, which is more convenient for applications. The general ...
Added: February 11, 2026
Shaykin D. V., A.M. Kamchatnov, Physical Review A: Atomic, Molecular, and Optical physics 2025 Vol. 112 No. 6 Article 063511
We develop the theory of dispersive shock waves in optical fibers for the case of long-distance propagation of optical pulses, when the small Raman effect stabilizes the profile of the shock. The Whitham modulation equations are derived as the basis for the Gurevich-Pitaevskii approach to the analytical theory of such shocks. We show that the wave variables at ...
Added: February 11, 2026
dos Santos G., Calasans de Brito L. F., Gammal A. et al., Physical Review A: Atomic, Molecular, and Optical physics 2025 Vol. 112 No. 3 Article 033318
A supersonic flow past an obstacle can generate a rich variety of wave excitations. This paper investigates, both analytically and numerically, two types of excitations generated by the flow of a Lee-Huang-Yang quantum fluid past an obstacle: linear radiation and oblique dark solitons. We show that wave crests of linear radiation can be accurately described by the proper ...
Added: February 11, 2026
Gromov E., Malomed B. A., Physics Letters A 2026 Vol. 567 Article 131219
We introduce an extended nonlinear Lugiato-Lefever equation (LLE) with the pseudo-stimulated-Raman-scattering (pseudo-SRS) cubic term, linear damping/gain, and spatial inhomogeneous (weekly or strongly localized) pump. The LLE is derived, in the extended adiabatic approximation, from the underlying Zakharov’s system (ZS), which includes a viscosity term acting on its low-frequency (LF) component and the pump supporting the ...
Added: November 28, 2025
Flamarion M. V., Pelinovsky E., Didenkulova E., Applied Mathematical Modelling 2025 Vol. 144 Article 116092
Algebraic soliton interactions with a periodic or quasi-periodic random force are investigated via the Benjamin-Ono equation, which models internal waves in a two-layer fluid. The random force is modeled as a Fourier series with a finite number of modes and random phases uniformly distributed, while its frequency spectrum has a Gaussian shape centered at a ...
Added: March 23, 2025
Pelinovsky E., Gurbatov S., Chaos, Solitons and Fractals 2025 Vol. 192 Article 116056
The statistical properties of a sequence of spaced solitons and compactons (soliton gas) with random amplitudes
and phases are studied based on the example of solitary waves – solutions of the generalized Korteweg-de Vries
equation with power nonlinearity (including fractional nonlinearity). Such sequences are used to specify initial
conditions in problems of modeling soliton turbulence. It is shown ...
Added: January 25, 2025
Kamchatnov A.M., Chaos 2023 Vol. 33 No. 9 Article 093105
We develop the theory of transformation of intensive initial nonlinear wave pulses to trains of solitons emerging at asymptotically large time of evolution. Our approach is based on the theory of dispersive shock waves in which the number of nonlinear oscillations in the shock becomes the number of solitons at the asymptotic state. We show ...
Added: January 22, 2025