Modulation and Amplitude Equations on Bounded Domains for Nonlinear SPDEs Driven by Cylindrical $\alpha$-stable Lévy Processes

In the present work, we establish approximation via modulation or amplitude equations of nonlinear stochastic partial differential equation (SPDE) driven by cylindrical $\alpha$-stable Lévy processes. We study SPDEs with a cubic nonlinearity, where deterministic is close to change stability trivial solution. The natural separation time scales this bifurcation allows us obtain an describing essential dynamics bifurcating pattern, thus reducing original infinite dimensional simpler finite effective dynamics. presence multiplicative stable noise that preserves constant solution impact on approximation. contrast Gaussian noise, due averaging effects nondominant patterns are uniformly small in time, large jumps might lead error terms, and new estimates needed take into account.