In this paper, we explored new families of solitary wave solutions of stochastic Chaffee-Infante equation (SCIE) with Wiener process in Itô sense. SCIE is one of the most important models in mathematical physics used to describe the processes of diffusion and wave propagation. Efficient $ (G'/G) $-expansion and its version generalized $ (r+G'/G) $-expansion are applied to obtain explicit solitary wave solutions to the targeted SCIE. The strategic $ (G'/G) $-expansion method originally converts SCIE to nonlinear ordinary differential equation (NODE) by wave transformation and then converts it to a set of nonlinear algebraic equations on the assumption of finite series-form solutions. Under the analysis of the solutions of the resulting system with Maple, a number of solitary wave solutions in the form of trigonometric, hyperbolic, and rational functions were found. To verify the presence of solitary wave solutions, such as soliton, dark, bright, kink, and anti-kink solitary wave solutions in SCIEs, several solitary wave solutions were evaluated using illustrated 3D visualizations for given parameter values under zero and nonzero noise effects. The implication of our results extends widely across various fields both in stochastic phenomena and nonlinear dynamics and has a contributions to physics and nonlinear science.
Citation: Hussain Gissy, Qasem M Tawhari. Innovative examination of noise impacts on explicit solitary wave solutions of (2+1)-dimensional stochastic Chaffee-Infante equation[J]. AIMS Mathematics, 2026, 11(1): 2954-2978. doi: 10.3934/math.2026118
In this paper, we explored new families of solitary wave solutions of stochastic Chaffee-Infante equation (SCIE) with Wiener process in Itô sense. SCIE is one of the most important models in mathematical physics used to describe the processes of diffusion and wave propagation. Efficient $ (G'/G) $-expansion and its version generalized $ (r+G'/G) $-expansion are applied to obtain explicit solitary wave solutions to the targeted SCIE. The strategic $ (G'/G) $-expansion method originally converts SCIE to nonlinear ordinary differential equation (NODE) by wave transformation and then converts it to a set of nonlinear algebraic equations on the assumption of finite series-form solutions. Under the analysis of the solutions of the resulting system with Maple, a number of solitary wave solutions in the form of trigonometric, hyperbolic, and rational functions were found. To verify the presence of solitary wave solutions, such as soliton, dark, bright, kink, and anti-kink solitary wave solutions in SCIEs, several solitary wave solutions were evaluated using illustrated 3D visualizations for given parameter values under zero and nonzero noise effects. The implication of our results extends widely across various fields both in stochastic phenomena and nonlinear dynamics and has a contributions to physics and nonlinear science.
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Figures(8)
Hussain Gissy, Qasem M Tawhari. Innovative examination of noise impacts on explicit solitary wave solutions of (2+1)-dimensional stochastic Chaffee-Infante equation[J]. AIMS Mathematics, 2026, 11(1): 2954-2978. doi: 10.3934/math.2026118
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