Unveiling the Transformative Power: Exploring the Nonlocal Potential Approach in the (3 + 1)-Dimensional Yu–Toda–Sasa–Fukuyama Equation
This paper focuses on the investigation of the Yu–Toda–Sasa–Fukuyama (YTSF) equation in its three-dimensional form. Based on the well-known Euler operator, a set of seven non-singular local multipliers is explored. Using these seven non-singular multipliers, the corresponding local conservation laws...
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2025-04-01
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| author | Enas Y. Abu El Seoud Ahmed S. Rashed Samah M. Mabrouk |
| author_facet | Enas Y. Abu El Seoud Ahmed S. Rashed Samah M. Mabrouk |
| author_sort | Enas Y. Abu El Seoud |
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| description | This paper focuses on the investigation of the Yu–Toda–Sasa–Fukuyama (YTSF) equation in its three-dimensional form. Based on the well-known Euler operator, a set of seven non-singular local multipliers is explored. Using these seven non-singular multipliers, the corresponding local conservation laws are derived. Additionally, an auxiliary potential-related system of partial differential equations (PDEs) is constructed. This study delves into nonlocal systems, which reveal numerous intriguing exact solutions of the YTSF equation. The nonlinear systems exhibit stable structures such as kink solitons, representing transitions, and breather or multi-solitons, modeling localized energy packets and complex interactions. These are employed in materials science, optics, communications, and plasma. Additionally, patterns such as parabolic backgrounds with ripples inform designs involving structured or varying media such as waveguides. |
| format | Article |
| id | doaj-art-bb93b759029a4dfa9244dd1334be00fb |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-bb93b759029a4dfa9244dd1334be00fb2025-08-20T02:17:25ZengMDPI AGAxioms2075-16802025-04-0114429810.3390/axioms14040298Unveiling the Transformative Power: Exploring the Nonlocal Potential Approach in the (3 + 1)-Dimensional Yu–Toda–Sasa–Fukuyama EquationEnas Y. Abu El Seoud0Ahmed S. Rashed1Samah M. Mabrouk2Department of Physics and Engineering Mathematics, Faculty of Engineering, Zagazig University, Zagazig 44519, EgyptDepartment of Physics and Engineering Mathematics, Faculty of Engineering, Zagazig University, Zagazig 44519, EgyptDepartment of Physics and Engineering Mathematics, Faculty of Engineering, Zagazig University, Zagazig 44519, EgyptThis paper focuses on the investigation of the Yu–Toda–Sasa–Fukuyama (YTSF) equation in its three-dimensional form. Based on the well-known Euler operator, a set of seven non-singular local multipliers is explored. Using these seven non-singular multipliers, the corresponding local conservation laws are derived. Additionally, an auxiliary potential-related system of partial differential equations (PDEs) is constructed. This study delves into nonlocal systems, which reveal numerous intriguing exact solutions of the YTSF equation. The nonlinear systems exhibit stable structures such as kink solitons, representing transitions, and breather or multi-solitons, modeling localized energy packets and complex interactions. These are employed in materials science, optics, communications, and plasma. Additionally, patterns such as parabolic backgrounds with ripples inform designs involving structured or varying media such as waveguides.https://www.mdpi.com/2075-1680/14/4/298nonlocal potential similaritylie infinitesimalsconservative lawsYTSF equation |
| spellingShingle | Enas Y. Abu El Seoud Ahmed S. Rashed Samah M. Mabrouk Unveiling the Transformative Power: Exploring the Nonlocal Potential Approach in the (3 + 1)-Dimensional Yu–Toda–Sasa–Fukuyama Equation Axioms nonlocal potential similarity lie infinitesimals conservative laws YTSF equation |
| title | Unveiling the Transformative Power: Exploring the Nonlocal Potential Approach in the (3 + 1)-Dimensional Yu–Toda–Sasa–Fukuyama Equation |
| title_full | Unveiling the Transformative Power: Exploring the Nonlocal Potential Approach in the (3 + 1)-Dimensional Yu–Toda–Sasa–Fukuyama Equation |
| title_fullStr | Unveiling the Transformative Power: Exploring the Nonlocal Potential Approach in the (3 + 1)-Dimensional Yu–Toda–Sasa–Fukuyama Equation |
| title_full_unstemmed | Unveiling the Transformative Power: Exploring the Nonlocal Potential Approach in the (3 + 1)-Dimensional Yu–Toda–Sasa–Fukuyama Equation |
| title_short | Unveiling the Transformative Power: Exploring the Nonlocal Potential Approach in the (3 + 1)-Dimensional Yu–Toda–Sasa–Fukuyama Equation |
| title_sort | unveiling the transformative power exploring the nonlocal potential approach in the 3 1 dimensional yu toda sasa fukuyama equation |
| topic | nonlocal potential similarity lie infinitesimals conservative laws YTSF equation |
| url | https://www.mdpi.com/2075-1680/14/4/298 |
| work_keys_str_mv | AT enasyabuelseoud unveilingthetransformativepowerexploringthenonlocalpotentialapproachinthe31dimensionalyutodasasafukuyamaequation AT ahmedsrashed unveilingthetransformativepowerexploringthenonlocalpotentialapproachinthe31dimensionalyutodasasafukuyamaequation AT samahmmabrouk unveilingthetransformativepowerexploringthenonlocalpotentialapproachinthe31dimensionalyutodasasafukuyamaequation |