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<p>This paper investigates the influence of additive noise and variable coefficients on the exact solutions of the (2+1)-dimensional stochastic Burgers’ equation. Firstly, the variable-coefficient stochastic Burgers’ equation is transformed into a coupled system comprising a (2+1)-dimensional Burgers-type equation with variable coefficients and solvable stochastic ordinary differential equations. Secondly, the exact soliton solution of the deterministic Burgers-type equation is derived through the combined application of the Painlevé analytic method and the Homogeneous balance method. By integrating this solution with the exact solution of the stochastic ordinary differential equations, the exact solutions of the target stochastic Burgers’ equation is obtained. Numerical simulations are conducted using the stochastic Zabusky–Kruskal finite difference scheme, demonstrating the efficacy of the proposed approach. Furthermore, the synergistic effects of varying coefficients and noise intensities on soliton dynamics are explored, providing insights into the interplay between stochastic perturbations and nonlinear wave phenomena.</p>

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Effects of additive white noise and variable coefficients on the exact solutions of the (2+1)-dimensional stochastic Burgers’ equation

  • 期刊论文

  • 发表日期：

    2025年7月28日

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  • Jiamin Shi,
  • Changzhao Li,
  • Chuanjian Wang,
  • Maojie Cai

摘要

This paper investigates the influence of additive noise and variable coefficients on the exact solutions of the (2+1)-dimensional stochastic Burgers’ equation. Firstly, the variable-coefficient stochastic Burgers’ equation is transformed into a coupled system comprising a (2+1)-dimensional Burgers-type equation with variable coefficients and solvable stochastic ordinary differential equations. Secondly, the exact soliton solution of the deterministic Burgers-type equation is derived through the combined application of the Painlevé analytic method and the Homogeneous balance method. By integrating this solution with the exact solution of the stochastic ordinary differential equations, the exact solutions of the target stochastic Burgers’ equation is obtained. Numerical simulations are conducted using the stochastic Zabusky–Kruskal finite difference scheme, demonstrating the efficacy of the proposed approach. Furthermore, the synergistic effects of varying coefficients and noise intensities on soliton dynamics are explored, providing insights into the interplay between stochastic perturbations and nonlinear wave phenomena.