Applications of Riccati–Bernoulli and Bäcklund Methods to the Kuralay-II System in Nonlinear Sciences
The Kuralay-II system (K-IIS) plays a pivotal role in modeling sophisticated nonlinear wave processes, particularly in the field of optics. This study introduces novel soliton solutions for the K-IIS, derived using the Riccati–Bernoulli sub-ODE method combined with Bäcklund transformation and confor...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-12-01
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| Series: | Mathematics |
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| author | Khudhayr A. Rashedi Musawa Yahya Almusawa Hassan Almusawa Tariq S. Alshammari Adel Almarashi |
| author_facet | Khudhayr A. Rashedi Musawa Yahya Almusawa Hassan Almusawa Tariq S. Alshammari Adel Almarashi |
| author_sort | Khudhayr A. Rashedi |
| collection | DOAJ |
| description | The Kuralay-II system (K-IIS) plays a pivotal role in modeling sophisticated nonlinear wave processes, particularly in the field of optics. This study introduces novel soliton solutions for the K-IIS, derived using the Riccati–Bernoulli sub-ODE method combined with Bäcklund transformation and conformable fractional derivatives. The obtained solutions are expressed in trigonometric, hyperbolic, and rational forms, highlighting the adaptability and efficacy of the proposed approach. To enhance the understanding of the results, the solutions are visualized using 2D representations for fractional-order variations and 3D plots for integer-type solutions, supported by detailed contour plots. The findings contribute to a deeper understanding of nonlinear wave–wave interactions and the underlying dynamics governed by fractional-order derivatives. This work underscores the significance of fractional calculus in analyzing complex wave phenomena and provides a robust framework for further exploration in nonlinear sciences and optical wave modeling. |
| format | Article |
| id | doaj-art-f892b22765f646bba01f7a5cb3033c09 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-f892b22765f646bba01f7a5cb3033c092025-01-10T13:18:12ZengMDPI AGMathematics2227-73902024-12-011318410.3390/math13010084Applications of Riccati–Bernoulli and Bäcklund Methods to the Kuralay-II System in Nonlinear SciencesKhudhayr A. Rashedi0Musawa Yahya Almusawa1Hassan Almusawa2Tariq S. Alshammari3Adel Almarashi4Deparment of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi ArabiaDeparment of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi ArabiaThe Kuralay-II system (K-IIS) plays a pivotal role in modeling sophisticated nonlinear wave processes, particularly in the field of optics. This study introduces novel soliton solutions for the K-IIS, derived using the Riccati–Bernoulli sub-ODE method combined with Bäcklund transformation and conformable fractional derivatives. The obtained solutions are expressed in trigonometric, hyperbolic, and rational forms, highlighting the adaptability and efficacy of the proposed approach. To enhance the understanding of the results, the solutions are visualized using 2D representations for fractional-order variations and 3D plots for integer-type solutions, supported by detailed contour plots. The findings contribute to a deeper understanding of nonlinear wave–wave interactions and the underlying dynamics governed by fractional-order derivatives. This work underscores the significance of fractional calculus in analyzing complex wave phenomena and provides a robust framework for further exploration in nonlinear sciences and optical wave modeling.https://www.mdpi.com/2227-7390/13/1/84Bäcklund transformationRiccati–Bernoulli sub-ODE methodfractional Kuralay-II system (K-IIS)solitary wave solutions |
| spellingShingle | Khudhayr A. Rashedi Musawa Yahya Almusawa Hassan Almusawa Tariq S. Alshammari Adel Almarashi Applications of Riccati–Bernoulli and Bäcklund Methods to the Kuralay-II System in Nonlinear Sciences Mathematics Bäcklund transformation Riccati–Bernoulli sub-ODE method fractional Kuralay-II system (K-IIS) solitary wave solutions |
| title | Applications of Riccati–Bernoulli and Bäcklund Methods to the Kuralay-II System in Nonlinear Sciences |
| title_full | Applications of Riccati–Bernoulli and Bäcklund Methods to the Kuralay-II System in Nonlinear Sciences |
| title_fullStr | Applications of Riccati–Bernoulli and Bäcklund Methods to the Kuralay-II System in Nonlinear Sciences |
| title_full_unstemmed | Applications of Riccati–Bernoulli and Bäcklund Methods to the Kuralay-II System in Nonlinear Sciences |
| title_short | Applications of Riccati–Bernoulli and Bäcklund Methods to the Kuralay-II System in Nonlinear Sciences |
| title_sort | applications of riccati bernoulli and backlund methods to the kuralay ii system in nonlinear sciences |
| topic | Bäcklund transformation Riccati–Bernoulli sub-ODE method fractional Kuralay-II system (K-IIS) solitary wave solutions |
| url | https://www.mdpi.com/2227-7390/13/1/84 |
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