Stochastic solutions of the geophysical KdV equation: Numerical simulations and white noise impact
This research explored stochastic soliton and periodic wave (SPW) solutions for the geophysical Korteweg-de Vries (KdV) equation with variable coefficients, incorporating the effects of Earth's rotation, fluid stratification, and topographical variations. The classical KdV equation, widely used...
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| Format: | Article |
| 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.2025269 |
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| author | Areej A. Almoneef Abd-Allah Hyder Mohamed A. Barakat Abdelrheem M. Aly |
| author_facet | Areej A. Almoneef Abd-Allah Hyder Mohamed A. Barakat Abdelrheem M. Aly |
| author_sort | Areej A. Almoneef |
| collection | DOAJ |
| description | This research explored stochastic soliton and periodic wave (SPW) solutions for the geophysical Korteweg-de Vries (KdV) equation with variable coefficients, incorporating the effects of Earth's rotation, fluid stratification, and topographical variations. The classical KdV equation, widely used to model nonlinear wave propagation, was extended to describe geophysical wave dynamics in atmospheric and oceanic systems. Exact solutions for both the deterministic and Wick-type stochastic (W-TS) forms of the geophysical KdV equation were obtained using white noise (WN) theory, the Hermite transform (HT), and the exp-function method. By employing the HT, the stochastic equation was transformed into a deterministic counterpart, facilitating the derivation of novel SPW solutions expressed as rational functions involving exponential terms. The inverse HT is then applied to retrieve stochastic SPW solutions under Gaussian WN conditions. Numerical analysis highlights the influence of Brownian motion (B-M) on the formation and behavior of SPWs in geophysical settings. Additionally, numerical simulations illustrate how random fluctuations affect wave stability and evolution, offering deeper insights into nonlinear wave interactions in oceanic and atmospheric environments. |
| format | Article |
| id | doaj-art-e107d411e41c40f08da8dbb3e389df48 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-e107d411e41c40f08da8dbb3e389df482025-08-20T02:08:20ZengAIMS PressAIMS Mathematics2473-69882025-03-011035859587910.3934/math.2025269Stochastic solutions of the geophysical KdV equation: Numerical simulations and white noise impactAreej A. Almoneef0Abd-Allah Hyder1Mohamed A. Barakat2Abdelrheem M. Aly3Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematics, College of Science, King Khalid University, Box 9004, 61413, Abha, Saudi ArabiaDepartment of Basic Science, University College of Alwajh, University of Tabuk, Saudi ArabiaDepartment of Mathematics, College of Science, King Khalid University, Box 9004, 61413, Abha, Saudi ArabiaThis research explored stochastic soliton and periodic wave (SPW) solutions for the geophysical Korteweg-de Vries (KdV) equation with variable coefficients, incorporating the effects of Earth's rotation, fluid stratification, and topographical variations. The classical KdV equation, widely used to model nonlinear wave propagation, was extended to describe geophysical wave dynamics in atmospheric and oceanic systems. Exact solutions for both the deterministic and Wick-type stochastic (W-TS) forms of the geophysical KdV equation were obtained using white noise (WN) theory, the Hermite transform (HT), and the exp-function method. By employing the HT, the stochastic equation was transformed into a deterministic counterpart, facilitating the derivation of novel SPW solutions expressed as rational functions involving exponential terms. The inverse HT is then applied to retrieve stochastic SPW solutions under Gaussian WN conditions. Numerical analysis highlights the influence of Brownian motion (B-M) on the formation and behavior of SPWs in geophysical settings. Additionally, numerical simulations illustrate how random fluctuations affect wave stability and evolution, offering deeper insights into nonlinear wave interactions in oceanic and atmospheric environments.https://www.aimspress.com/article/doi/10.3934/math.2025269geophysical kdv equationsoliton and periodic wave solutionswhite noise effectsexp-function methodnumerical simulations |
| spellingShingle | Areej A. Almoneef Abd-Allah Hyder Mohamed A. Barakat Abdelrheem M. Aly Stochastic solutions of the geophysical KdV equation: Numerical simulations and white noise impact AIMS Mathematics geophysical kdv equation soliton and periodic wave solutions white noise effects exp-function method numerical simulations |
| title | Stochastic solutions of the geophysical KdV equation: Numerical simulations and white noise impact |
| title_full | Stochastic solutions of the geophysical KdV equation: Numerical simulations and white noise impact |
| title_fullStr | Stochastic solutions of the geophysical KdV equation: Numerical simulations and white noise impact |
| title_full_unstemmed | Stochastic solutions of the geophysical KdV equation: Numerical simulations and white noise impact |
| title_short | Stochastic solutions of the geophysical KdV equation: Numerical simulations and white noise impact |
| title_sort | stochastic solutions of the geophysical kdv equation numerical simulations and white noise impact |
| topic | geophysical kdv equation soliton and periodic wave solutions white noise effects exp-function method numerical simulations |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025269 |
| work_keys_str_mv | AT areejaalmoneef stochasticsolutionsofthegeophysicalkdvequationnumericalsimulationsandwhitenoiseimpact AT abdallahhyder stochasticsolutionsofthegeophysicalkdvequationnumericalsimulationsandwhitenoiseimpact AT mohamedabarakat stochasticsolutionsofthegeophysicalkdvequationnumericalsimulationsandwhitenoiseimpact AT abdelrheemmaly stochasticsolutionsofthegeophysicalkdvequationnumericalsimulationsandwhitenoiseimpact |