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Article
Publication date: 6 August 2024

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

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…

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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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 34 no. 10
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 7 June 2023

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

The purpose of this study is to form a linear structure of components of the modified Korteweg–De Vries (mKdV) hierarchy. The new model includes 3rd order standard mKdV equation…

91

Abstract

Purpose

The purpose of this study is to form a linear structure of components of the modified Korteweg–De Vries (mKdV) hierarchy. The new model includes 3rd order standard mKdV equation, 5th order and 7th order mKdV equations.

Design/methodology/approach

The authors investigate Painlevé integrability of the constructed linear structure.

Findings

The Painlevé analysis demonstrates that established sum of integrable models retains the integrability of each component.

Research limitations/implications

The research also presents a set of rational schemes of trigonometric and hyperbolic functions to derive breather solutions.

Practical implications

The authors also furnish a variety of solitonic solutions and complex solutions as well.

Social implications

The work formally furnishes algorithms for extending integrable equations that consist of components of a hierarchy.

Originality/value

The paper presents an original work for developing Painlevé integrable model via using components of a hierarchy.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

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