Investigating exact solutions for the (3+1)-dimensional KdV-CBS equation: A non-traveling wave approach
Non-traveling wave solutions are crucial, as they provide deeper insights into the complex dynamics and diverse wave structures of nonlinear systems, expanding the understanding of phenomena beyond traditional traveling wave approaches. This research focuses on deriving explicit non-traveling wave s...
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| Language: | English |
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AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025314 |
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| author | Shami A. M. Alsallami |
| author_facet | Shami A. M. Alsallami |
| author_sort | Shami A. M. Alsallami |
| collection | DOAJ |
| description | Non-traveling wave solutions are crucial, as they provide deeper insights into the complex dynamics and diverse wave structures of nonlinear systems, expanding the understanding of phenomena beyond traditional traveling wave approaches. This research focuses on deriving explicit non-traveling wave solutions for the (3+1)-dimensional KdV–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation. A new method using an improved variable separation technique is applied to find abundant explicit non-traveling wave solutions. This technique integrates elements from both the KdV and CBS equations, extending and unifying previous methodologies. The derived solutions incorporate multiple arbitrary functions, showcasing greater versatility than previous methodologies. By selecting specific forms for these functions, diverse non-traveling exact solutions such as periodic solitary waves and cross soliton-like patterns are constructed. All derived solutions are validated by plugging them into the original equation using Maple software, confirming their correctness. Since non-traveling wave solutions for the (3+1)-dimensional KdV-CBS equation have not been thoroughly explored, this study makes a significant contribution to the field. |
| format | Article |
| id | doaj-art-e48a5300df74490abb6ccb483e81d84a |
| institution | DOAJ |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-e48a5300df74490abb6ccb483e81d84a2025-08-20T03:16:58ZengAIMS PressAIMS Mathematics2473-69882025-03-011036853687210.3934/math.2025314Investigating exact solutions for the (3+1)-dimensional KdV-CBS equation: A non-traveling wave approachShami A. M. Alsallami0Mathematics Department, College of Sciences, Umm Al-Qura University, Makkah 24381, Saudi ArabiaNon-traveling wave solutions are crucial, as they provide deeper insights into the complex dynamics and diverse wave structures of nonlinear systems, expanding the understanding of phenomena beyond traditional traveling wave approaches. This research focuses on deriving explicit non-traveling wave solutions for the (3+1)-dimensional KdV–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation. A new method using an improved variable separation technique is applied to find abundant explicit non-traveling wave solutions. This technique integrates elements from both the KdV and CBS equations, extending and unifying previous methodologies. The derived solutions incorporate multiple arbitrary functions, showcasing greater versatility than previous methodologies. By selecting specific forms for these functions, diverse non-traveling exact solutions such as periodic solitary waves and cross soliton-like patterns are constructed. All derived solutions are validated by plugging them into the original equation using Maple software, confirming their correctness. Since non-traveling wave solutions for the (3+1)-dimensional KdV-CBS equation have not been thoroughly explored, this study makes a significant contribution to the field.https://www.aimspress.com/article/doi/10.3934/math.2025314modified generalized variable separation techniquenon-traveling solutionsymbolic computationkdv–calogero–bogoyavlenskii–schiff equation |
| spellingShingle | Shami A. M. Alsallami Investigating exact solutions for the (3+1)-dimensional KdV-CBS equation: A non-traveling wave approach AIMS Mathematics modified generalized variable separation technique non-traveling solution symbolic computation kdv–calogero–bogoyavlenskii–schiff equation |
| title | Investigating exact solutions for the (3+1)-dimensional KdV-CBS equation: A non-traveling wave approach |
| title_full | Investigating exact solutions for the (3+1)-dimensional KdV-CBS equation: A non-traveling wave approach |
| title_fullStr | Investigating exact solutions for the (3+1)-dimensional KdV-CBS equation: A non-traveling wave approach |
| title_full_unstemmed | Investigating exact solutions for the (3+1)-dimensional KdV-CBS equation: A non-traveling wave approach |
| title_short | Investigating exact solutions for the (3+1)-dimensional KdV-CBS equation: A non-traveling wave approach |
| title_sort | investigating exact solutions for the 3 1 dimensional kdv cbs equation a non traveling wave approach |
| topic | modified generalized variable separation technique non-traveling solution symbolic computation kdv–calogero–bogoyavlenskii–schiff equation |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025314 |
| work_keys_str_mv | AT shamiamalsallami investigatingexactsolutionsforthe31dimensionalkdvcbsequationanontravelingwaveapproach |