On exact solutions for the stochastic time fractional Gardner equation

Abstract

In this work, the stochastic time fractional Gardner equation is analysed. Some white noise functional solutions for this equation are obtained by using white noise analysis, Hermite transforms and the modified fractional sub-equation method. These solutions include exact stochastic trigonometric functions, hyperbolic functions solutions and wave solutions.

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

“…With the help of inverse χ-Hermite transform, we also showed an example of how the stochastic solutions can be given as a functional solution for non-Gussian white noise. Note that in mathematical physics, the schema proposed in this paper can be used to solve several non-linear equations of evolution [10][11][12][13][14][15].…”

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

“…The study of (3+1)-Dimensional non-linear equations is thriving as these equations model the real features in a wide array of fields of science, technology, fluid mechanics, wave propagation, electrodynamics, and engineering [5][6][7][8][9]. Recently, Khater et al [10], Korpinar et al [11,12], have addressed the applications non-linear wave equations in mathematical physics [13][14][15]. In this paper, we aim to obtain non-Gaussian solutions for stochastic (3+1)-dimensional modified BBM equations of the χ-Wick-type.…”

Solitons and other nonlinear waves for stochastic Schrödinger‐Hirota model using improved modified extended tanh‐function approach

“…Previous studies have employed stochastic nonlinear Schrödinger equations to describe the behavior of stochastic optical solitons in nonlinear media. These equations have been extensively discussed in literature, with references such as [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”