On numerical-analytical methods for solving the Cauchy problem for stochastic Korteweg-de Vries equations

The Korteweg–de Vries equation is a nonlinear third-order partial differential equation central to wave theory and commonly studied through inverse scattering. This seminar addresses the less extensively developed stochastic setting, focusing on the Cauchy problem for a generalized equation with noise in its nonlinear term.

The noise is expressed through a symmetric integral with an arbitrary continuous integrator. This construction generalizes both Stieltjes integration and Stratonovich integration against a Wiener process. The proposed numerical methods extend Strang splitting and BCH schemes to stochastic Korteweg–de Vries equations. The presentation also examines existence, uniqueness and stability of solutions, and formulates a change-point problem for detecting shifts in the underlying regime from observations.