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The article examines mythopoetics in Sasha Sokolov’s novels A School for Fools and Palisandria. In the 20th century authors widely turn to neo-mythologism in its various manifestations – from the myth-making of prose writers and poets of the beginning of the century to the nationalfolklore type of mythologism in the prose of the era of stagnation. In Sokolov’s novels, the fi rst branch of the development of mythopoetics continues in the form of modernist myth in A School for Fools and postmodern deconstruction of myth in Palisandria. The article shows that Sokolov’s first and last novels have contrasting forms of mythology. In A School for Fools, via a cyclic chronotope, the author models the ontological myth of eternal return, in which the main mythologems are metamorphoses and the author’s mythologem of the Sender of the Wind. In this myth, the creator is the main character of the novel. In Palisandria the opposite process is observed – the dispelling of the myth of eternal return and the formation of the myth of “timelessness” through numerous simulacra-incarnations of the main character. The author of the article talks about the change in the principles of mythologization from the fi rst to the third novel – from the ontological myth of A School for Fools Sokolov comes to the deconstruction of myth and postmodern negation in Palisandria. Sokolov’s novels are deeply mythopoetic. In his work, Sokolov repeatedly turns to mythological images and allusions from classical myths, as well as literary archetypes. Based on all of the above, it can be argued that neomythologism is one of the main principles of Sokolov’s oeuvre. Using the example of Sasha Sokolov’s texts, the article shows one of the ways of transforming neomythologism from modernism to postmodernism.

In this study, we present two meshless schemes, namely the radial basis function (RBF) method and the polynomial method, for the numerical investigation of the time-fractional Harry Dym equation and the Drinfeld-Sokolov-Wilson system. In both methods, the temporal derivatives are estimated using the Caputo operator, while the spatial derivatives are approximated either through radial basis functions or polynomials. Additionally, a collocation approach is employed to convert the system of equations into a system of linear equations that is easier to solve. The accuracy of the methods is assessed by calculating the $ L_{\infty} $ error norm, and the outcomes are displayed through tables and figures. The simulation results indicate that both methods exhibit strong performance in handling the fractional partial differential equations (PDEs) under investigation.

In this paper, we define a N=2 multi-component supersymmetric B type 2KP(MS2BKP) hierarchy and its additional symmetries. These additional flows form a B type multi SW1+∞ Lie algebra. Under a reduction, we derive a N=2 multi-component supersymmetric D type Drinfeld–Sokolov hierarchy which has a multi super Virasoro algebraic structure.

The aim of this paper is to study the nonlinear couple Drinfel’d–Sokolov–Wilson (DSW) equation under conformable differential operator (CDO) that plays an important role in describing the shallow water in fluid mechanics, plasma physics, nonlinear optics and Bose–Einstein condensate (soliton formation). The Tanh–Coth and energy balance techniques are implemented in this work to explore some travelling wave solutions. These analytical methods yield various solutions for the considered DSW equation. The solutions obtained from both method are expressed in the form of hyperbolic and trigonometric function. Furthermore, the dynamic behaviour of the obtained solutions are illustrated, via 2D and 3D curves. Additionally, the effect of the conformable differential operator on dynamics of wave solutions is studied via 2D graphs.

The article is devoted to the 85th anniversary of the outstanding scientist in the field of accounting, doctor of economic sciences, honored worker of science of Russian Federation, professor Yaroslav Vyacheslavovich Sokolov (1938–2010). The authors made an attempt to review the multifaceted scientific and pedagogical activities of the scientist over nearly 50 years. The authors analyze Sokolov’s ideas in the field of accounting, as well as his contribution to the creation of certain areas (the Sokolov school); his works in the field of history, which won him universal recognition, among which a special place is given to his republished work «Treatise on Accounts and Records» by Luca Pacioli; the social and educational activities of the scientist on the background of changing economy in the country and in the world are shown. An attempt has been made to assess comprehensively the role of Professor Sokolov in the formation of the process of training specialists in accounting, analysis and audit, as well as statistics.

A seventh order ordinary differential equation (ODE) arising by reduction of the Drinfeld-Sokolov hierarchyis shown to be identical to a similarity reduction of an equationin the hierarchy of Sawada-Kotera.We also exhibit its link with a particular F-VI,a fourth order ODE isolated by Cosgrove which is likely to define a higher order Painlev\'e function.

Abstract This article delves into the dynamic constructions of distinctive traveling wave solutions for wave circulation in shallow water mechanics, specifically addressing the time-fractional couple Drinfel’d–Sokolov–Wilson (DSW) equation. Introducing the previously untapped $$exp(-\phi (\xi ))$$ e x p ( - ϕ ( ξ ) ) -expansion method, we successfully generate a diverse set of analytic solutions expressed in hyperbolic, trigonometric, and rational functions, each with permitted parameters. Visualization through three-dimensional (3D) as well two-dimensional (2D) plots, including contour plots, reveals inherent wave phenomena in the DSW equation. These newly obtained wave solutions serve as a catalyst for refining theories in applied science, offering a means to validate mathematical simulations for the proliferation of waves in shallow water as well as other nonlinear scenarios. Obtained wave solutions demonstrate the bright soliton, periodic, multiple soliton, and kink soliton shape. The simplicity and efficacy of the implemented methods are demonstrated, providing a valuable tool for approximating the considered equation. All figures are devoted to demonstrate the complete wave futures of the attained solutions to the studied equation with the collaboration of specific selections of the chosen parameters. Moreover, it may have summarized that the attained wave solutions and their physical phenomena might be useful to comprehend the various kind of wave propagation in mathematical physics and engineering.

The generalized Drinfeld-Sokolov system is a widely-used model that describes wave phenomena in various contexts. Many properties of this system, such as Hamiltonian formulations and integrability, have been extensively studied and exact solutions have been derived for specific cases. In this paper we applied the direct method of multipliers to obtain all low-order local conservation laws of the system. These conservation laws correspond to physical quantities that remain constant over time, such as energy and momentum, and we provided a physical interpretation for each of them. Additionally, we investigated the Lie point symmetries and first-order symmetries of the system. Through the point symmetries and constructing the optimal systems of one-dimensional subalgebras, we were able to reduce the system of partial differential equations to ordinary differential systems and obtain new solutions for the system.

Book review on Milan Řípa, Ronald Richter: Termojaderná fúze první na světě: Sokolov 1936, Muzeum Sokolov, příspěvková organizace Karlovarského kraje, Sokolov 2021, 67 stran, ISBN 978-80-86630-47-2

The time-fractional coupled Drinfel’d–Sokolov–Wilson (DSW) equation is pivotal in soliton theory, especially for water wave mechanics. Its precise description of soliton phenomena in dispersive water waves makes it widely applicable in fluid dynamics and related fields like tsunami prediction, mathematical physics, and plasma physics. In this study, we present novel soliton solutions for the DSW equation, which significantly enhance the accuracy of describing soliton phenomena. To achieve these results, we employed two distinct methods to derive the solutions: the Sardar subequation method, which works with one variable, and the Ω′Ω, 1Ω method which utilizes two variables. These approaches supply significant improvements in efficiency, accuracy, and the ability to explore a broader spectrum of soliton solutions compared to traditional computational methods. By using these techniques, we construct a wide range of wave structures, including rational, trigonometric, and hyperbolic functions. Rigorous validation with Mathematica software 13.1 ensures precision, while dynamic visual representations illustrate soliton solutions with diverse patterns such as dark solitons, multiple dark solitons, singular solitons, multiple singular solitons, kink solitons, bright solitons, and bell-shaped patterns. These findings highlight the effectiveness of these methods in discovering new soliton solutions and supplying deeper insights into the DSW model’s behavior. The novel soliton solutions obtained in this study significantly enhance our understanding of the DSW equation’s underlying dynamics and offer potential applications across various scientific fields.

In this article, the coupled Drinfeld–Sokolov–Wilson equation under investigation base on computational approach named extension of modified rational expansion approach. By this computational approach secured various kinds of solitons named kink solitons, dark solitons, anti kink solitons, periodic solitons, bright solitons, kink dark solitons, kink bright solitons, anti kink dark solitons, anti kink bright solitons for coupled DSW system. The calculated results are interesting, precise, novel, and different which have not been secured in the previous research. We represent the graphical behaviour of determined solutions by 2-D, 3-D and contour through computational software. The determined results may helpful and play significant role in the study of nonlinear behaviour in various branches of physical sciences such as laser optics, communication system, fluid dynamics, transfer of heat, shallow water waves, acoustics, optics and many others. The constructed results prove that proposed computational approach is concise, powerful, and straightforward for securing the solitons results of other nonlinear partial differential equations.

We report a new batch of wave solutions for the coupled Drinfel’d–Sokolov–Wilson equation which represents a coupled system of nonlinear partial differential equations (NLPDEs). Firstly by making a travelling wave ansatz, we decouple the system and obtain a second-order ordinary differential equation (ODE). Thereafter we perform phase space and bifurcation analysis of that second-order ODE and proceed to construct the general solution for the envelope of the wave packet. The solutions are expressed in terms of the Jacobi elliptic sine function from which one can obtain solitary wave (particular) solutions by imposing appropriate conditions on the roots of certain quartic polynomials as discussed thereafter.

The coupled Drinfeld–Sokolov–Wilson (DSW) equation is a system of nonlinear partial differential equations (NLPDEs) in (1+1)-dimensions that play a fundamental role in soliton theory and integrable systems. Due to its ability to accurately describe wave phenomena in dispersive water waves, coupled DSW equation has wide-ranging applications in fluid dynamics, plasma physics, and mathematical physics. This study investigates the solitary wave solution of coupled DSW equation by using ϕ6-model expansion. This technique reveals the diverse types of solutions, including bright, dark, singular, and periodic singular solitons. The 3D, contour, and 2D plots are also illustrated to demonstrate the physical behavior of the obtained solutions. The findings of this study can contribute to the development of new analytical and numerical tools for solving other nonlinear equations in the future. The inclusion of constraint conditions in the ϕ6-model expansion technique enhances its applicability and reliability, rendering it a valuable approach for investigating nonlinear systems in various scientific domains.

In this work, we mainly investigate the Drinfeld-Sokolov system by employing the functional variable method. Some new solitary wave and periodic solutions are successfully derived. The dynamic characteristics of these obtained solitary wave solutions are elaborated by plotting some 3-D and 2-D figure. [ABSTRACT FROM AUTHOR]

The review analyses A.M. Sokolov’s monograph “1944: The crushing blows of the Red Army” dedicated to the description of the offensive operations of 1944 which received the name of “Ten Stalin’s blows” in Soviet historiography. The proposed review examines the structure of the book, the sources used by the author when writing the monograph, the logic of presenting the material, and proposes advantages and disadvantages of the work. In conclusion, the author of the review finds that the information presented in the book can be used in teaching military history in educational organizations as well as for the patriotic education of the younger generation.

The review evaluates the book by literary critic and historian Professor B.V. Sokolov, dedicated to the fate of Soviet writers who associated themselves with the White Movement. The work under review makes an attempt to highlight previously little-known episodes of the participation of writers in the Civil War, who were forced for the time being to hide certain pages of their past. It was found that the restoration of authentic biographies faces methodological difficulties.

The stochastic-fractional Drinfel’d–Sokolov–Wilson equation is a presently improved nonlinear partial differential equation in electromagnetism and fluid mechanics. Using the theory of planar dynamical systems, the authors first analyzed chaotic behavior, including sensitivity, Poincaré section and Lyapunov exponent, and then constructed solitary waves and periodic solutions. Secondly, the author analyzed the effects of random noise and fractional derivatives on the solution. Finally, a comparative study was conducted to demonstrate the innovation of this study. The methods and results of this paper can be applied to the study of a wider range of nonlinear wave phenomena.

We adopted the Lie symmetry technique to obtain some new exact waveform solutions for the coupled Drinfeld Sokolov Wilson (DSW) system. This system emerges from phenomena such as water waves, theoretical physics, fluid dynamics, biology, and chemical sciences. We use the Jacobi elliptic function (JEF) method to deal with some of the reduced systems during the symmetry reductions, which reveals rational, exponential, and hyperbolic functions based waveform solutions. The properties of these solutions indicate that these are periodic waves, solitary waves, double periodic waves, and shock wave solutions. Several of the answers that have been found are entirely new and might be important for researchers to recognize. By assigning specific values to parameters, some chosen solutions are graphically validated. This method can be applied more broadly to handle several different types of nonlinear evolution systems.

Abstract This paper aims to analyze the coupled nonlinear fractional Drinfel’d-Sokolov-Wilson (FDSW) model with beta derivative. The nonlinear FDSW equation plays an important role in describing dispersive water wave structures in mathematical physics and engineering, which is used to describe nonlinear surface gravity waves propagating over horizontal sea bed. We have applied the travelling wave transformation that converts the FDSW model to nonlinear ordinary differential equations. After that, we applied the generalized rational exponential function method (GERFM). Diverse types of soliton solution structures in the form of singular bright, periodic, dark, bell-shaped and trigonometric functions are attained via the proposed method. By selecting a suitable parametric value, the 3D, 2D and contour plots for some solutions are also displayed to visualize their nature in a better way. The modulation instability for the model is also discussed. The results show that the presented method is simple and powerful to get a novel soliton solution for nonlinear PDEs.

Within the context of fractional calculus, we investigate novel mathematical possibilities. In this context, using the fractional dispersion relations for the fractional wave equation, we explore a class of the generalized fractional wave equation numerically. Some important classes of differential equations in the theory of wave studies are Drinfeld–Sokolov–Wilson and Shallow Water equations. In this effort, the natural transform decomposition technique has been implemented to investigate the explicit result of fractional-order coupled schemes of Drinfeld–Sokolov–Wilson and Shallow Water coupled systems. The proposed method is obtained by coupling the Natural transform with the Adomian decomposition process. The current technique significantly works to find the approximate solution without any discretization or constraining parameter assumptions. The obtained numerical and graphical outcomes by the devised technique are compared with the available exact result to verify the convergence of the method. For mathematical calculations, the Mathematica software package is used. [ABSTRACT FROM AUTHOR]

The modified extended tanh technique is used to investigate the conformable time fractional Drinfel'd-Sokolov-Wilson (DSW) equation and integrate some precise and explicit solutions in this survey. The DSW equation was invented in fluid dynamics. The modified extended tanh technique executes to integrate the nonlinear DSW equation for achieve diverse solitonic and traveling wave envelops. Because of this, trigonometric, hyperbolic and rational solutions have been found with a few acceptable parameters. The dynamical behaviors of the obtained solutions in the pattern of the kink, bell, multi-wave, kinky lump, periodic lump, interaction lump, and kink wave types have been illustrated with 3D and density plots for arbitrary chose of the permitted parameters. By characterizing the particular benefits of the exemplified boundaries by the portrayal of sketches and by deciphering the actual events, we have laid out acceptable soliton plans and managed the actual significance of the acquired courses of action. New precise voyaging wave arrangements are unambiguously gained with the aid of symbolic computation using the procedures that have been announced. Therefore, the obtained outcomes expose that the projected schemes are very operative, easier and efficient on realizing natures of waves and also introducing new wave strategies to a diversity of NLEEs that occur within the engineering sector.

This study is used to investigate the exact explicit solutions and dynamical behaviors of the (1+1)-dimensional integrable system of Drinfel’d–Sokolov–Wilson equations in dispersive media. Firstly, the unified method is implemented to find explicit solutions in polynomial and rational forms. These solutions include rational, dark and bright soliton structures. After that, the planar dynamical system of the considered model is obtained using the Galilean transformation. The phase portraits of the bifurcations are drawn from the planar dynamical system for different physical parametric values using the fourth-order Runge–Kutta method. Further, an external force is imposed on the dynamical system to observe the phase portraits of chaotic trajectories. These tracks are outlined for different values of the strength and frequency of the external force acting on the dynamical system. The outcomes show that a given model has chaotic behvior as its solution becomes disordered by taking small variation in the strength and frequency of the external force. The results are new and can be helpful in investigating the dynamical behaviors of the other nonlinear physical models arising in optics, bio-mathematics and so many other fields of science.

In this article, we successfully obtain novel solutions for the coupled Drinfel’d–Sokolov–Wilson DSW system utilizing various methods. These include soliton solutions characterized by hyperbolic, rational, and trigonometric functions. Specifically, the generalized exponential rational function method (GERFM) and a modified version of the new Kudryashov method (MVNK) are employed to derive diverse soliton solutions for the system. Additionally, we demonstrate numerical solutions for the coupled Drinfel’d–Sokolov–Wilson system using adaptive moving mesh and uniform mesh methods. Also, we study the stability and error analysis of the numerical schemes. To validate the accuracy and reliability of the exact solutions obtained through analytical methods, we compare them with the numerical solutions both analytically and graphically. The techniques presented in this article are deemed suitable and acceptable and can be effectively applied to solve other nonlinear evolution systems.