Study of a combined Kairat-II-X equation: Painlevé integrability, multiple kink, lump and other physical solutions

IF 4 3区工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

International Journal of Numerical Methods for Heat & Fluid Flow Pub Date : 2024-08-06 DOI:10.1108/hff-05-2024-0411

Abdul-Majid Wazwaz, Weaam Alhejaili, Samir El-Tantawy

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引用次数: 0

Abstract

Purpose

This study aims to explore a novel model that integrates the Kairat-II equation and Kairat-X equation (K-XE), denoted as the Kairat-II-X (K-II-X) equation. This model demonstrates the connections between the differential geometry of curves and the concept of equivalence.

Design/methodology/approach

The Painlevé analysis shows that the combined K-II-X equation retains the complete Painlevé integrability.

Findings

This study explores multiple soliton (solutions in the form of kink solutions with entirely new dispersion relations and phase shifts.

Research limitations/implications

Hirota’s bilinear technique is used to provide these novel solutions.

Practical implications

This study also provides a diverse range of solutions for the K-II-X equation, including kink, periodic and singular solutions.

Social implications

This study provides formal procedures for analyzing recently developed systems that investigate optical communications, plasma physics, oceans and seas, fluid mechanics and the differential geometry of curves, among other topics.

Originality/value

The study introduces a novel Painlevé integrable model that has been constructed and delivers valuable discoveries.

查看原文本刊更多论文

凯拉特-II-X 组合方程研究：潘列维可积分性、多重扭结、肿块和其他物理解决方案

目的本研究旨在探索一种整合了凯拉特-II方程和凯拉特-X方程（K-XE）的新模型，称为凯拉特-II-X（K-II-X）方程。该模型展示了曲线微分几何与等价概念之间的联系。研究结果该研究以具有全新分散关系和相移的扭结解的形式探索了多个孤子（解）。实践意义本研究还为 K-II-X 方程提供了多种解，包括扭结解、周期解和奇异解。社会意义本研究为分析最近开发的系统提供了正式程序，这些系统研究了光通信、等离子体物理、海洋、流体力学和曲线微分几何等主题。原创性/价值本研究介绍了一个新颖的潘列维可积分模型，该模型已经构建并带来了有价值的发现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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