A time-splitting spectral method for the generalized Zakharov system in multi-dimensions

The generalized Zakharov system (ZS) couples a dispersive field E (scalar or vectorial) and J nondispersive fields {n(j)}(j-1)(J) with a progating speed of 1/epsilon(j). In this paper, we extend our one-dimensional time-splitting spectral method (TSSP) for the generalized ZS into higher dimension. A main new idea is to reformulate the multi-dimensional wave equations for the nondispersive fields into a first-order system using a change of variable defined in the Fourier space. The proposed scheme TSSP is unconditionally stable, second-order in time and spectrally accurate in space. Moreover, in the subsonic regime, it allows numerical capturing of the subsonic limit without resolving the small parameters epsilon(j). Numerical examples confirm these properties of this method.