New Solitary Wave Solutions of the Lakshamanan–Porsezian–Daniel Model with the Application of the Φ<sup>6</sup> Method in Fractional Sense

New Solitary Wave Solutions of the Lakshamanan–Porsezian–Daniel Model with the Application of the Φ<sup>6</sup> Method in Fractional Sense

This paper explores a significant fractional model, which is the fractional Lakshamanan–Porsezian–Daniel (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">FLPD</mi></se...

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Bibliographic Details
Main Authors: Hicham Saber, Hussien Albala, Khaled Aldwoah, Amer Alsulami, Khidir Shaib Mohamed, Mohammed Hassan, Abdelkader Moumen
Format: Article
Language:English
Published: MDPI AG 2024-12-01
Series:Fractal and Fractional
Subjects:
factional Lakshamanan–Porsezian–Daniel model
conformable derivative
Φ<sup>6</sup> technique
soliton solutions
stability analysis
Online Access:https://www.mdpi.com/2504-3110/9/1/10
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Summary:This paper explores a significant fractional model, which is the fractional Lakshamanan–Porsezian–Daniel (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">FLPD</mi></semantics></math></inline-formula>) model, widely used in various fields like nonlinear optics and plasma physics. An advanced analytical solution for it is attained by the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="sans-serif">Φ</mi><mn>6</mn></msup></semantics></math></inline-formula> technique. According to this methodology, effective and accurate solutions for wave structures within various types can be produced in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">FLPD</mi></semantics></math></inline-formula> model framework. Solutions such as dark, bright, singular, periodic, and plane waves are studied in detail to identify their stability and behavior. Validations are also brought forward to assess the precision and flexibility of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="sans-serif">Φ</mi><mn>6</mn></msup></semantics></math></inline-formula> technique in modeling fractional models. Therefore, it is established in this study that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="sans-serif">Φ</mi><mn>6</mn></msup></semantics></math></inline-formula> technique represents a powerful tool for examining wave patterns in differential fractional order models.
ISSN:2504-3110

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