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Öğe Analytical investigation of space–time shifted nonlocal stochastic Sasa–Satsuma equation using the enhanced modified extended tanh-expansion method for stochastic solitary waves Solutions(Elsevier B.V., 2024) Manzoor, Zuha; Ashraf, Farrah; Iqbal, Muhammad Sajid; Akgül, Ali; Misro, Md YushalifyIn this paper, discover exact solutions of the space–time shifted nonlocal stochastic Sasa–Satsuma equations using the enhanced modified extended tanh-expansion method. This method is a sophisticated mathematical approach for analytical and approximate solution of a nonlinear partial differential equations. The space–time shifted nonlocal stochastic Sasa–Satsuma equations define the behavior of two complex-valued functions, u and v, in a nonlinear system. These equations are complicated to solve analytically because they contain a number of components that describe space–time shifting, nonlocal interactions, and stochastic problems. To increase reliability and effectiveness of the solutions, this method couples the extended tanh-function method with an enhanced method. In order to demonstrate how white noise affects the solutions to the space–time shifted nonlocal stochastic Sasa–Satsuma equations, we also use Matlab to create 3D surfaces and contour graphs of exact solutions. © 2024 The Author(s)Öğe Analyzing multiplicative noise effects on stochastic dynamical ?4 equation using the new extended direct algebraic method(Elsevier, 2024) Manzoor, Zuha; Iqbal, Muhammad Sajid; Omer, Nader; Zakarya, Mohammed; Kanan, Mohammad; Akgul, Ali; Hussain, ShabbirThe stochastic dynamical phi(4) equation is obtained by adding a multiplicative noise term to the classical phi(4) equation. The noise term represents the random fluctuations that are present in the system and is modeled by a Wiener process. The stochastic dynamical phi(4) equation is a powerful tool for modeling the behavior of complex systems that exhibit randomness and nonlinearity. It has a wide range of applications in physics, chemistry, biology, and finance. Our goal of this paper is to use the new extended direct algebraic method to find the stochastic traveling wave solutions of the dynamical phi(4) equation. We explore the new trigonometric, hyperbolic, and rational functions using the new extended direct algebraic method. Furthermore, we use Matlab to plot 3D surfaces of exact solutions to show how multiplicative noise affects the solutions to the stochastic dynamical phi(4) equation.