Modelling the Formation and Propagation of Nonlinear Waves in Dynamical Systems with Sources
The problem of describing the dynamics of wave processes in hydrodynamic systems with sources remains generally open. The known results in constructing the corresponding models do not have sufficient generality and are applicable to the analysis of real systems only under special restrictions on the...
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| Format: | Article |
| Language: | English |
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AIDIC Servizi S.r.l.
2025-07-01
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| Series: | Chemical Engineering Transactions |
| Online Access: | https://www.cetjournal.it/index.php/cet/article/view/15441 |
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| author | Meirim Amantay Arnold Brener Madina Balabekova Kamil Kayumov Akhmet Musabekov |
| author_facet | Meirim Amantay Arnold Brener Madina Balabekova Kamil Kayumov Akhmet Musabekov |
| author_sort | Meirim Amantay |
| collection | DOAJ |
| description | The problem of describing the dynamics of wave processes in hydrodynamic systems with sources remains generally open. The known results in constructing the corresponding models do not have sufficient generality and are applicable to the analysis of real systems only under special restrictions on the explicit form of a function for the source intensity. The absence of solution-constants for unperturbed flows in the presence of a mass source creates challenges for the effective use of asymptotic analysis methods. Another challenge is associated with the possibility of a delayed response to flow disturbances introduced by the source.
The main objective of this paper is to develop a fairly general mathematical model allowing for identifying a set of parameters for controlling the propagation of nonlinear wave processes in dynamic systems with sources without specifying an explicit form of the source function.
To solve the problem, the paper develops approaches based on the adaptation of methods for deriving the perturbed Korteweg-de-Vries equation taking into account the nonlocality of the response based on the Whitham integro-differential equation. The contribution and novelty of this work are that a general concept of a mathematical model for describing the formation and propagation of nonlinear waves in systems with sources has been submitted, and the asymptotic analysis to establish the main control parameters has been performed too. The results of the work may be useful in the theory and practice of controlling heat and mass transfer processes in through-flowing reactors. |
| format | Article |
| id | doaj-art-18bb07106b0c44b9831a205fabaf2896 |
| institution | DOAJ |
| issn | 2283-9216 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | AIDIC Servizi S.r.l. |
| record_format | Article |
| series | Chemical Engineering Transactions |
| spelling | doaj-art-18bb07106b0c44b9831a205fabaf28962025-08-20T02:46:35ZengAIDIC Servizi S.r.l.Chemical Engineering Transactions2283-92162025-07-01117Modelling the Formation and Propagation of Nonlinear Waves in Dynamical Systems with SourcesMeirim AmantayArnold BrenerMadina BalabekovaKamil KayumovAkhmet MusabekovThe problem of describing the dynamics of wave processes in hydrodynamic systems with sources remains generally open. The known results in constructing the corresponding models do not have sufficient generality and are applicable to the analysis of real systems only under special restrictions on the explicit form of a function for the source intensity. The absence of solution-constants for unperturbed flows in the presence of a mass source creates challenges for the effective use of asymptotic analysis methods. Another challenge is associated with the possibility of a delayed response to flow disturbances introduced by the source. The main objective of this paper is to develop a fairly general mathematical model allowing for identifying a set of parameters for controlling the propagation of nonlinear wave processes in dynamic systems with sources without specifying an explicit form of the source function. To solve the problem, the paper develops approaches based on the adaptation of methods for deriving the perturbed Korteweg-de-Vries equation taking into account the nonlocality of the response based on the Whitham integro-differential equation. The contribution and novelty of this work are that a general concept of a mathematical model for describing the formation and propagation of nonlinear waves in systems with sources has been submitted, and the asymptotic analysis to establish the main control parameters has been performed too. The results of the work may be useful in the theory and practice of controlling heat and mass transfer processes in through-flowing reactors.https://www.cetjournal.it/index.php/cet/article/view/15441 |
| spellingShingle | Meirim Amantay Arnold Brener Madina Balabekova Kamil Kayumov Akhmet Musabekov Modelling the Formation and Propagation of Nonlinear Waves in Dynamical Systems with Sources Chemical Engineering Transactions |
| title | Modelling the Formation and Propagation of Nonlinear Waves in Dynamical Systems with Sources |
| title_full | Modelling the Formation and Propagation of Nonlinear Waves in Dynamical Systems with Sources |
| title_fullStr | Modelling the Formation and Propagation of Nonlinear Waves in Dynamical Systems with Sources |
| title_full_unstemmed | Modelling the Formation and Propagation of Nonlinear Waves in Dynamical Systems with Sources |
| title_short | Modelling the Formation and Propagation of Nonlinear Waves in Dynamical Systems with Sources |
| title_sort | modelling the formation and propagation of nonlinear waves in dynamical systems with sources |
| url | https://www.cetjournal.it/index.php/cet/article/view/15441 |
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