On the Cauchy Problem for Stochastic and Deterministic Generalized Burgers Equations

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.