Conformal multi-symplectic Fourier pseudo-spectral methods for stochastic damped Klein–Gordon–Schrödinger equations

Stochastic damped Klein–Gordon–Schrödinger (KGS) equations arise in the modeling of wave–field interactions under dissipation and random perturbations and possess intrinsic geometric structures. In this paper, we propose a structure-preserving Fourier pseudo-spectral scheme for the stochastic damped KGS system with additive noise. Spatial discretization is carried out by a Fourier pseudo-spectral method, while an exponential midpoint integrator is employed in time. The resulting fully discrete scheme preserves the stochastic conformal multi-symplectic structure and exactly reproduces the exponential charge dissipation law at the discrete level. A rigorous mean-square convergence analysis is established, showing that the proposed method achieves the convergence rate O(τ+J^−r) in the discrete L ²-norm, where τ and J denote the temporal and spatial resolutions, respectively. Numerical experiments in one and two dimensions confirm the theoretical results and demonstrate the accuracy, stability, and structure-preserving properties of the scheme.