Extended (3 + 1)-dimensional Kairat-II and Kairat-X equations: Painlevé integrability, multiple soliton solutions, lump solutions, and breather wave solutions

IF 4 3区工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS International Journal of Numerical Methods for Heat & Fluid Flow Pub Date : 2024-04-09 DOI:10.1108/hff-01-2024-0053

Abdul-Majid Wazwaz

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引用次数: 0

Abstract

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.

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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

研究目的本研究旨在探讨两个新开发的（3 + 1）维 Kairat-II 和 Kairat-X 方程，这两个方程说明了与曲线微分几何和等价方面的关系。研究结果本研究探讨了所研究的两个模型的多种孤子解。此外，作者还发现只有 Kairat-X 方程给出了块解和呼吸波解。研究局限/意义本研究使用 Hirota 双线性算法提供了多种具有有用物理结构的孤子解。此外，还从 Kairat-X 模型中得到了块解和呼吸波解。社会意义这项研究为研究等离子体物理、光通信、海洋和曲线微分几何等新构建的系统提供了正式的算法。原创性/价值本文是一项原创性工作，介绍了两个新开发的 Painlev\'{e} 可积分模型，并给出了深刻的结论。

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来源期刊

International Journal of Numerical Methods for Heat & Fluid Flow 工程技术-力学

CiteScore

9.50

自引率

11.90%

发文量

100

审稿时长

6-12 weeks

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