Stochastic solitons of a short-wave intermediate dispersive variable (SIdV) equation
It is necessary to utilize certain stochastic methods while finding the soliton solutions since several physical systems are by their very nature stochastic. By adding randomness into the modeling process, researchers gain deeper insights into the impact of uncertainties on soliton evolution, stabil...
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AIMS Press
2024-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024523?viewType=HTML |
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| author | Shabir Ahmad Saud Fahad Aldosary Meraj Ali Khan |
| author_facet | Shabir Ahmad Saud Fahad Aldosary Meraj Ali Khan |
| author_sort | Shabir Ahmad |
| collection | DOAJ |
| description | It is necessary to utilize certain stochastic methods while finding the soliton solutions since several physical systems are by their very nature stochastic. By adding randomness into the modeling process, researchers gain deeper insights into the impact of uncertainties on soliton evolution, stability, and interaction. In the realm of dynamics, deterministic models often encounter limitations, prompting the incorporation of stochastic techniques to provide a more comprehensive framework. Our attention was directed towards the short-wave intermediate dispersive variable (SIdV) equation with the Wiener process. By integrating advanced methodologies such as the modified Kudrayshov technique (KT), the generalized KT, and the sine-cosine method, we delved into the exploration of diverse solitary wave solutions. Through those sophisticated techniques, a spectrum of the traveling wave solutions was unveiled, encompassing both the bounded and singular manifestations. This approach not only expanded our understanding of wave dynamics but also shed light on the intricate interplay between deterministic and stochastic processes in physical systems. Solitons maintained stable periodicity but became vulnerable to increased noise, disrupting predictability. Dark solitons obtained in the results showed sensitivity to noise, amplifying variations in behavior. Furthermore, the localized wave patterns displayed sharp peaks and periodicity, with noise introducing heightened fluctuations, emphasizing stochastic influence on wave solutions. |
| first_indexed | 2024-04-24T15:37:01Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-24T15:37:01Z |
| publishDate | 2024-03-01 |
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| spelling | doaj.art-18802b503091490bbc8a149ad4d1a0492024-04-02T01:15:52ZengAIMS PressAIMS Mathematics2473-69882024-03-0195107171073310.3934/math.2024523Stochastic solitons of a short-wave intermediate dispersive variable (SIdV) equationShabir Ahmad0Saud Fahad Aldosary1Meraj Ali Khan 21. Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan2. Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia3. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P. O. Box-65892, Riyadh 11566, Saudi ArabiaIt is necessary to utilize certain stochastic methods while finding the soliton solutions since several physical systems are by their very nature stochastic. By adding randomness into the modeling process, researchers gain deeper insights into the impact of uncertainties on soliton evolution, stability, and interaction. In the realm of dynamics, deterministic models often encounter limitations, prompting the incorporation of stochastic techniques to provide a more comprehensive framework. Our attention was directed towards the short-wave intermediate dispersive variable (SIdV) equation with the Wiener process. By integrating advanced methodologies such as the modified Kudrayshov technique (KT), the generalized KT, and the sine-cosine method, we delved into the exploration of diverse solitary wave solutions. Through those sophisticated techniques, a spectrum of the traveling wave solutions was unveiled, encompassing both the bounded and singular manifestations. This approach not only expanded our understanding of wave dynamics but also shed light on the intricate interplay between deterministic and stochastic processes in physical systems. Solitons maintained stable periodicity but became vulnerable to increased noise, disrupting predictability. Dark solitons obtained in the results showed sensitivity to noise, amplifying variations in behavior. Furthermore, the localized wave patterns displayed sharp peaks and periodicity, with noise introducing heightened fluctuations, emphasizing stochastic influence on wave solutions.https://www.aimspress.com/article/doi/10.3934/math.2024523?viewType=HTMLkdv equationwiener processsoliton |
| spellingShingle | Shabir Ahmad Saud Fahad Aldosary Meraj Ali Khan Stochastic solitons of a short-wave intermediate dispersive variable (SIdV) equation AIMS Mathematics kdv equation wiener process soliton |
| title | Stochastic solitons of a short-wave intermediate dispersive variable (SIdV) equation |
| title_full | Stochastic solitons of a short-wave intermediate dispersive variable (SIdV) equation |
| title_fullStr | Stochastic solitons of a short-wave intermediate dispersive variable (SIdV) equation |
| title_full_unstemmed | Stochastic solitons of a short-wave intermediate dispersive variable (SIdV) equation |
| title_short | Stochastic solitons of a short-wave intermediate dispersive variable (SIdV) equation |
| title_sort | stochastic solitons of a short wave intermediate dispersive variable sidv equation |
| topic | kdv equation wiener process soliton |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024523?viewType=HTML |
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