{"title":"扩展 (3 + 1) 维 Kairat-II 和 Kairat-X 方程：潘列维可积分性、多重孤子解、块解和呼吸波解","authors":"Abdul-Majid Wazwaz","doi":"10.1108/hff-01-2024-0053","DOIUrl":null,"url":null,"abstract":"<h3>Purpose</h3>\n<p>This study aims to investigate two newly developed (3 + 1)-dimensional Kairat-II and Kairat-X equations that illustrate relations with the differential geometry of curves and equivalence aspects.</p><!--/ Abstract__block -->\n<h3>Design/methodology/approach</h3>\n<p>The Painlevé analysis confirms the complete integrability of both Kairat-II and Kairat-X equations.</p><!--/ Abstract__block -->\n<h3>Findings</h3>\n<p>This study explores multiple soliton solutions for the two examined models. Moreover, the author showed that only Kairat-X give lump solutions and breather wave solutions.</p><!--/ Abstract__block -->\n<h3>Research limitations/implications</h3>\n<p>The Hirota’s bilinear algorithm is used to furnish a variety of solitonic solutions with useful physical structures.</p><!--/ Abstract__block -->\n<h3>Practical implications</h3>\n<p>This study also furnishes a variety of numerous periodic solutions, kink solutions and singular solutions for Kairat-II equation. 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Moreover, the author showed that only Kairat-X give lump solutions and breather wave solutions.</p><!--/ Abstract__block -->\\n<h3>Research limitations/implications</h3>\\n<p>The Hirota’s bilinear algorithm is used to furnish a variety of solitonic solutions with useful physical structures.</p><!--/ Abstract__block -->\\n<h3>Practical implications</h3>\\n<p>This study also furnishes a variety of numerous periodic solutions, kink solutions and singular solutions for Kairat-II equation. 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Extended (3 + 1)-dimensional Kairat-II and Kairat-X equations: Painlevé integrability, multiple soliton solutions, lump solutions, and breather wave solutions
Purpose
This study aims to investigate two newly developed (3 + 1)-dimensional Kairat-II and Kairat-X equations that illustrate relations with the differential geometry of curves and equivalence aspects.
Design/methodology/approach
The Painlevé analysis confirms the complete integrability of both Kairat-II and Kairat-X equations.
Findings
This study explores multiple soliton solutions for the two examined models. Moreover, the author showed that only Kairat-X give lump solutions and breather wave solutions.
Research limitations/implications
The Hirota’s bilinear algorithm is used to furnish a variety of solitonic solutions with useful physical structures.
Practical implications
This study also furnishes a variety of numerous periodic solutions, kink solutions and singular solutions for Kairat-II equation. In addition, lump solutions and breather wave solutions were achieved from Kairat-X model.
Social implications
The work formally furnishes algorithms for studying newly constructed systems that examine plasma physics, optical communications, oceans and seas and the differential geometry of curves, among others.
Originality/value
This paper presents an original work that presents two newly developed Painlev\'{e} integrable models with insightful findings.
期刊介绍：
The main objective of this international journal is to provide applied mathematicians, engineers and scientists engaged in computer-aided design and research in computational heat transfer and fluid dynamics, whether in academic institutions of industry, with timely and accessible information on the development, refinement and application of computer-based numerical techniques for solving problems in heat and fluid flow. - See more at: http://emeraldgrouppublishing.com/products/journals/journals.htm?id=hff#sthash.Kf80GRt8.dpuf
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