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<p>A new method is developed for solving the Cauchy problem for stochastic and deterministic generalized Burgers equations with temporal noise in the nonlinear part of the equation.The solution to the stochastic generalized Burgers equation is represented as the Weierstrass transform of a function that is a solution to the Cauchy problem for the generalized Hopf equation.The obtained results remain valid for the deterministic generalized Burgers equation.</p>

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On the Cauchy Problem for Stochastic and Deterministic Generalized Burgers Equations

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • E. I. Zotova,
  • F. S. Nasyrov

摘要

A new method is developed for solving the Cauchy problem for stochastic and deterministic generalized Burgers equations with temporal noise in the nonlinear part of the equation.The solution to the stochastic generalized Burgers equation is represented as the Weierstrass transform of a function that is a solution to the Cauchy problem for the generalized Hopf equation.The obtained results remain valid for the deterministic generalized Burgers equation.