Analytical soliton solutions and stability of the stochastic potential KdV equation

Résumé fourni par la source

The main objective of this study is to explore the soliton dynamics of the Stochastic Potential Korteweg–de Vries (SPKdV) equation, a key model in nonlinear optical solitons, photon dynamics, electrical circuits, and multicomponent plasmas. Initially, we apply a wave transformation, which converts the third-order nonlinear PDE into a third-order ODE. Analytical solutions were obtained using the generalized Riccati equation mapping method. The effects of the stochastic term, dispersion coefficient, and nonlinearity coefficient were examined through graphical analysis. Three-dimensional, two-dimensional, and contour plots were generated in Maple (2024) to illustrate the influence of the stochastic parameter on the solutions. Finally, a stability analysis of the considered model is conducted to examine the robustness of the solutions.

Ce résumé expose les affirmations des auteurs. BNTIC ne l’interprète pas comme une validation indépendante des résultats.