Investigation of a Self-Similar Solution of the Stochastic Space-Fractional Kuramoto – Sivashinsky Equation in the Domain of Analyticity

The paper considers the stochastic space-fractional Kuramoto – Sivashinsky equation in the complex plane. This equation is reduced to an ordinary differential equation. For the resulting ODE, a theorem on the existence and uniqueness of the Cauchy problem in a neighborhood of the initial data is formulated and proved. For practical applications, an analytical approximate solution (a partial sum of a series) is proposed. A priori error estimates of the analytical approximate solution are provided. To extend beyond the domain of convergence of the series obtained, an analytic continuation of the approximate solution is carried out.