Exact Traveling Wave Solutions for Wick-Type Stochastic Schamel KdV Equation

Abstract

F-expansion method is proposed to seek exact solutions of nonlinear partial differential equations. By means of Hermite transform, inverse Hermite transform, and white noise analysis, the variable coefficients and Wick-type stochastic Schamel KdV equations are completely described. Abundant exact traveling wave solutions for variable coefficients Schamel KdV equations are given. These solutions include exact stochastic Jacobi elliptic functions, trigonometric functions, and hyperbolic functions solutions.

Hypercomplex systems and non-Gaussian stochastic solutions of χ-Wick-type (3+1)-dimensional modified Benjamin-Bona-Mahony equation

“…1, with variable coefficients. Through white noise functional analysis [16], Ghany [17,18], Ghany and Hyder [19][20][21][22], Ghany et al [23,24], Ghany and Zakarya [25,26], Hyder and Zakarya [27], Agarwal et al [28], Zakarya et al [29], Agarwal et al [30] studied this model of white noise functional solutions for some non-linear stochastic partial differential equations (SPDE) more intensively. In addition, Okb El Bab et al, [1] and Zakarya [3] explored some important topics related to the construction of non-Gaussian white noise analysis using the hyper-complex systems theory and some applications.…”

On exact solutions for the stochastic time fractional Gardner equation

“…Due to the fact that the stochastic models are more realistic than the deterministic models, we concentrate our study in this paper on the wick-type stochastic fractional Gardner equation with conformable fractional derivatives. Many more researches related to stochastic fractional differential equations [15][16][17][18]. In [15], firstis investigated the effects of external noise for the motion of solitons and investigated the diffusion of soliton of the KdV equation with the aid of Gaussian noise, which satisfies a diffusion equation in transformed coordinates.…”

“…In [15], firstis investigated the effects of external noise for the motion of solitons and investigated the diffusion of soliton of the KdV equation with the aid of Gaussian noise, which satisfies a diffusion equation in transformed coordinates. Ghany and Hyder [16] obtained analytical solutions stochastic time-fractional KdV equations with the wick-type, Ghany and Zakarya [17] obtained exact traveling wave solutions stochastic Schamel KdV equation with wick-type, in [18] is used white noise functional approach for the fractional coupled KdV equations and is obtained new soliton solutions.…”

Non-Gaussian Wick Calculus Based on Hypercomplex Systems

“…The classical white noise analysis (Gaussian white noise analysis) it is possible to understand as a theory of generalized functions of infinite many variables with pairing between test and generalized functions provided by integration with respect to the Gaussian measure. Recently, some authors as Okb El Bab, Zabel, Ghany and Hyder [10], Ghany [11], Ghany and Hyder [12,13,14], Ghany and Zakarya [15,16,17] and Ghany and Qurashi [18], studied some important subjects related to Gaussian white noise analysis. Also, Okb El Bab, Zabel and Ghany [26], introduced some studies of harmonic analysis in hypercomplex systems.…”