Analytical Solutions for Generalized Stochastic HSC-KdV Equations with Variable Coefficients Using Hermite Transform and F-Expansion Method Article Swipe
Mohammed Zakarya
,
Nadiah Zafer Al-Shehri
,
Hegagi Mohamed Ali
,
Mahmoud A. Abd-Rabo
,
Haytham M. Rezk
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.3390/axioms14080624
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.3390/axioms14080624
This study focuses on analyzing the generalized HSC-KdV equations characterized by variable coefficients and Wick-type stochastic (Wt.S) elements. To derive white noise functional (WNF) solutions, we employ the Hermite transform, the homogeneous balance principle, and the Fe (F-expansion) technique. Leveraging the inherent connection between hypercomplex system (HCS) theory and white noise (WN) analysis, we establish a comprehensive framework for exploring stochastic partial differential equations (PDEs) involving non-Gaussian parameters (N-GP). As a result, exact solutions expressed through Jacobi elliptic functions (JEFs) and trigonometric and hyperbolic forms are obtained for both the variable coefficients and stochastic forms of the generalized HSC-KdV equations. An illustrative example is included to validate the theoretical findings.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/axioms14080624
- https://www.mdpi.com/2075-1680/14/8/624/pdf?version=1755058653
- OA Status
- gold
- References
- 38
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4413127879
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https://openalex.org/W4413127879Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.3390/axioms14080624Digital Object Identifier
- Title
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Analytical Solutions for Generalized Stochastic HSC-KdV Equations with Variable Coefficients Using Hermite Transform and F-Expansion MethodWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2025Year of publication
- Publication date
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2025-08-10Full publication date if available
- Authors
-
Mohammed Zakarya, Nadiah Zafer Al-Shehri, Hegagi Mohamed Ali, Mahmoud A. Abd-Rabo, Haytham M. RezkList of authors in order
- Landing page
-
https://doi.org/10.3390/axioms14080624Publisher landing page
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https://www.mdpi.com/2075-1680/14/8/624/pdf?version=1755058653Direct link to full text PDF
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YesWhether a free full text is available
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goldOpen access status per OpenAlex
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https://www.mdpi.com/2075-1680/14/8/624/pdf?version=1755058653Direct OA link when available
- Concepts
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Hermite polynomials, Mathematics, Korteweg–de Vries equation, Applied mathematics, Variable (mathematics), Mathematical analysis, Nonlinear system, Physics, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| referenced_works | https://openalex.org/W2021773803, https://openalex.org/W6697997958, https://openalex.org/W6687686431, https://openalex.org/W2524971255, https://openalex.org/W2984429772, https://openalex.org/W2035106635, https://openalex.org/W2061339363, https://openalex.org/W2086488349, https://openalex.org/W1982754700, https://openalex.org/W2019007415, https://openalex.org/W1633315028, https://openalex.org/W2033739016, https://openalex.org/W2006607804, https://openalex.org/W2047807008, https://openalex.org/W1996820401, https://openalex.org/W1980178787, https://openalex.org/W2045776586, https://openalex.org/W2028337553, https://openalex.org/W2068981255, https://openalex.org/W649798762, https://openalex.org/W6727714058, https://openalex.org/W2015664794, https://openalex.org/W6704164431, https://openalex.org/W1534302984, https://openalex.org/W6740579433, https://openalex.org/W4230211289, https://openalex.org/W2512209573, https://openalex.org/W2247216366, https://openalex.org/W1486929028, https://openalex.org/W2022646987, https://openalex.org/W2621244846, https://openalex.org/W3093997535, https://openalex.org/W4309686613, https://openalex.org/W2525609638, https://openalex.org/W2309468965, https://openalex.org/W2197887806, https://openalex.org/W2340171337, https://openalex.org/W2724980447 |
| referenced_works_count | 38 |
| abstract_inverted_index.a | 55, 70 |
| abstract_inverted_index.An | 100 |
| abstract_inverted_index.As | 69 |
| abstract_inverted_index.Fe | 36 |
| abstract_inverted_index.To | 18 |
| abstract_inverted_index.by | 10 |
| abstract_inverted_index.is | 103 |
| abstract_inverted_index.of | 95 |
| abstract_inverted_index.on | 3 |
| abstract_inverted_index.to | 105 |
| abstract_inverted_index.we | 25, 53 |
| abstract_inverted_index.and | 13, 34, 48, 80, 82, 92 |
| abstract_inverted_index.are | 85 |
| abstract_inverted_index.for | 58, 87 |
| abstract_inverted_index.the | 5, 27, 30, 35, 40, 89, 96, 107 |
| abstract_inverted_index.(WN) | 51 |
| abstract_inverted_index.This | 0 |
| abstract_inverted_index.both | 88 |
| abstract_inverted_index.(HCS) | 46 |
| abstract_inverted_index.(WNF) | 23 |
| abstract_inverted_index.exact | 72 |
| abstract_inverted_index.forms | 84, 94 |
| abstract_inverted_index.noise | 21, 50 |
| abstract_inverted_index.study | 1 |
| abstract_inverted_index.white | 20, 49 |
| abstract_inverted_index.(JEFs) | 79 |
| abstract_inverted_index.(PDEs) | 64 |
| abstract_inverted_index.(Wt.S) | 16 |
| abstract_inverted_index.Jacobi | 76 |
| abstract_inverted_index.derive | 19 |
| abstract_inverted_index.employ | 26 |
| abstract_inverted_index.system | 45 |
| abstract_inverted_index.theory | 47 |
| abstract_inverted_index.(N-GP). | 68 |
| abstract_inverted_index.HSC-KdV | 7, 98 |
| abstract_inverted_index.Hermite | 28 |
| abstract_inverted_index.balance | 32 |
| abstract_inverted_index.between | 43 |
| abstract_inverted_index.example | 102 |
| abstract_inverted_index.focuses | 2 |
| abstract_inverted_index.partial | 61 |
| abstract_inverted_index.result, | 71 |
| abstract_inverted_index.through | 75 |
| abstract_inverted_index.elliptic | 77 |
| abstract_inverted_index.included | 104 |
| abstract_inverted_index.inherent | 41 |
| abstract_inverted_index.obtained | 86 |
| abstract_inverted_index.validate | 106 |
| abstract_inverted_index.variable | 11, 90 |
| abstract_inverted_index.Wick-type | 14 |
| abstract_inverted_index.analysis, | 52 |
| abstract_inverted_index.analyzing | 4 |
| abstract_inverted_index.elements. | 17 |
| abstract_inverted_index.equations | 8, 63 |
| abstract_inverted_index.establish | 54 |
| abstract_inverted_index.exploring | 59 |
| abstract_inverted_index.expressed | 74 |
| abstract_inverted_index.findings. | 109 |
| abstract_inverted_index.framework | 57 |
| abstract_inverted_index.functions | 78 |
| abstract_inverted_index.involving | 65 |
| abstract_inverted_index.solutions | 73 |
| abstract_inverted_index.Leveraging | 39 |
| abstract_inverted_index.connection | 42 |
| abstract_inverted_index.equations. | 99 |
| abstract_inverted_index.functional | 22 |
| abstract_inverted_index.hyperbolic | 83 |
| abstract_inverted_index.parameters | 67 |
| abstract_inverted_index.principle, | 33 |
| abstract_inverted_index.solutions, | 24 |
| abstract_inverted_index.stochastic | 15, 60, 93 |
| abstract_inverted_index.technique. | 38 |
| abstract_inverted_index.transform, | 29 |
| abstract_inverted_index.generalized | 6, 97 |
| abstract_inverted_index.homogeneous | 31 |
| abstract_inverted_index.theoretical | 108 |
| abstract_inverted_index.coefficients | 12, 91 |
| abstract_inverted_index.differential | 62 |
| abstract_inverted_index.hypercomplex | 44 |
| abstract_inverted_index.illustrative | 101 |
| abstract_inverted_index.non-Gaussian | 66 |
| abstract_inverted_index.(F-expansion) | 37 |
| abstract_inverted_index.characterized | 9 |
| abstract_inverted_index.comprehensive | 56 |
| abstract_inverted_index.trigonometric | 81 |
| cited_by_percentile_year | |
| corresponding_author_ids | https://openalex.org/A5004188579 |
| countries_distinct_count | 2 |
| institutions_distinct_count | 5 |
| corresponding_institution_ids | https://openalex.org/I184834183 |
| citation_normalized_percentile.value | 0.27427096 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |