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Abstract
In this paper, we apply stochastic differential equations with the Wiener process to investigate the soliton solutions of the Chaffee–Infante (CI) equation. The CI equation, a fundamental model in mathematical physics, explains concepts such as wave propagation and diffusion processes. Exact soliton solutions are obtained through the application of the modified extended tanh (MET) method. The obtained wave figures in 3D, 2D, and contour are highly localized and determine an individual frequency shift under the behavior of sharp peak, periodic wave, and singular soliton. The MET method shows to be a valuable analytical tool for obtaining soliton solutions, essential for understanding the dynamics of nonlinear wave phenomena. Numerical simulations enable us to explore soliton solutions in two and three dimensions, shedding light on their properties over time. Our results have wide applications in various domains, including stochastic processes and nonlinear dynamics, impacting advancements in physics, engineering, finance, biology, and beyond.
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1 University of Malakand, Department of Mathematics, Chakdara, Dir Lower, Pakistan (GRID:grid.440567.4) (ISNI:0000 0004 0607 0608)
2 Northern Border University, Department of Chemical and Materials Engineering, College of Engineering, Arar, Saudi Arabia (GRID:grid.449533.c) (ISNI:0000 0004 1757 2152)
3 University of Ha’il, Department of Mechanical Engineering, College of Engineering, Ha’il City, Saudi Arabia (GRID:grid.443320.2) (ISNI:0000 0004 0608 0056); University of Monastir, Department of Energy Engineering, College of Engineering, Laboratory of Metrology and Energy systems, Monastir, Tunisia (GRID:grid.411838.7) (ISNI:0000 0004 0593 5040)
4 King Khalid University, Department of Mathematics,College of Science, Abha, Saudi Arabia (GRID:grid.412144.6) (ISNI:0000 0004 1790 7100)
5 University of Campania “Luigi Vanvitelli”, Department of Mathematics and Physics, Caserta, Italy (GRID:grid.9841.4) (ISNI:0000 0001 2200 8888)
6 Laghman University, Department of Physics, Mehtarlam City, Afghanistan (GRID:grid.9841.4)