Analytical Solutions for Generalized Stochastic HSC-KdV Equations with Variable Coefficients Using Hermite Transform and F-Expansion Method

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....

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Veröffentlicht in:Axioms Jg. 14; H. 8; S. 624
Hauptverfasser: Zakarya, Mohammed, Al-Shehri, Nadiah Zafer, Ali, Hegagi M., Abd-Rabo, Mahmoud A., Rezk, Haytham M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 10.08.2025
Schlagworte:
Algebra
Differential equations
Elliptic functions
Exact solutions
F-expansion technique
generalized HSC-KdV equations
Hermite transform
Korteweg-Devries equation
Mathematical functions
Methods
non-Gaussian parameters
Nonlinear equations
Ordinary differential equations
Partial differential equations
Physics
Quantum field theory
White noise
white noise functional approach
Wick-type stochastic analysis
ISSN:2075-1680, 2075-1680
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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content type line 14
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms14080624