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Dynamical analysis of the (3+1)-dimensional extended Kairat-X equation: analysing the interaction paradigms.

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Title: Dynamical analysis of the (3+1)-dimensional extended Kairat-X equation: analysing the interaction paradigms.
Authors: Asadullah, Mohammad1 (AUTHOR), Javid, Ahmad1 (AUTHOR), Chahlaoui, Younes2 (AUTHOR), Raza, Nauman3 (AUTHOR), Bekir, Ahmet4 (AUTHOR) bekirahmet@gmail.com
Source: Pramana: Journal of Physics. Mar2026, Vol. 100 Issue 1, p1-14. 14p.
Subjects: Solitons, Nonlinear wave equations, Wave equation, Nonlinear analysis, Partial differential equations
Abstract: This work investigates the newly proposed integrable (3+1)-dimensional (3D) extended Kairat-X equation. By incorporating Hirota's bilinear form, various lump and interaction solutions such as periodic-lump interaction, 1-stripe, periodic and lump interaction, 1-stripe-lump interaction, etc. are obtained. Along with these lump interaction solutions, various other types such as wave-type solutions, kink-cross rational solutions and solitary wave solutions are also investigated. Additionally, the innovative soliton-type solutions are provided by the extended transformed rational function technique, which uses the Hirota bilinear representation of the governing model. To highlight the physical features of these solutions, 3D and density plots are generated with the aid of interactive software which gave us a better understanding of the results. These solutions provide a comprehensive study of the dynamical behaviour of novel nonlinear Kairat-X equation. [ABSTRACT FROM AUTHOR]
Copyright of Pramana: Journal of Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: This work investigates the newly proposed integrable (3+1)-dimensional (3D) extended Kairat-X equation. By incorporating Hirota's bilinear form, various lump and interaction solutions such as periodic-lump interaction, 1-stripe, periodic and lump interaction, 1-stripe-lump interaction, etc. are obtained. Along with these lump interaction solutions, various other types such as wave-type solutions, kink-cross rational solutions and solitary wave solutions are also investigated. Additionally, the innovative soliton-type solutions are provided by the extended transformed rational function technique, which uses the Hirota bilinear representation of the governing model. To highlight the physical features of these solutions, 3D and density plots are generated with the aid of interactive software which gave us a better understanding of the results. These solutions provide a comprehensive study of the dynamical behaviour of novel nonlinear Kairat-X equation. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Pramana: Journal of Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s12043-025-03059-3
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        Text: English
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      – SubjectFull: Nonlinear wave equations
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      – SubjectFull: Wave equation
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      – SubjectFull: Partial differential equations
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              Text: Mar2026
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