A reproducible FFT-based Strang-splitting baseline for the generalized Davey-Stewartson system

We present a reproducible FFT-based Strang-splitting baseline for the generalized Davey–Stewartson system (GDSS), a three-component nonlocal model that couples a complex short-wave envelope to two real long-wave fields. In the classical two-component Davey–Stewartson system the long-wave field is recovered with a single scalar Fourier multiplier. In the GDSS the cross-coupling links the two long-wave potentials through a non-diagonal [Formula: see text] Fourier symbol, and the existing numerical studies, based on first-order splitting or implicit finite differences, have addressed only blow-up detection. Here the mode-wise inversion of this symbol is folded into one precomputed multiplier acting on the filtered intensity, so the coupled recovery adds no transforms to the time loop. The linear dispersive subflow is integrated exactly in Fourier space and the nonlinear, nonlocal subflow is a pointwise phase rotation, with density dealiasing and zero-mode normalization. The scheme is assessed through invariant drift, boundary effects, temporal and spatial resolution, cost, a manufactured solution with both long-wave fields active, and exact Babaoglu–Erbay traveling waves. Recovery residuals stay near round-off, mass and momentum drift by about [Formula: see text], and the energy drift, of order [Formula: see text], is the splitting error of the Strang composition; over a ten times longer horizon it settles to a plateau that scales as [Formula: see text]. The cost per step matches that of the classical two-component scheme. The results give a reproducible reference for GDSS simulations and a baseline for future invariant-preserving schemes.