Asymptotic preserving trigonometric integrators for the quantum Zakharov system

We present a new class of asymptotic preserving trigonometric integrators for the quantum Zakharov system. Their convergence holds in the strong quantum regime $\vartheta =1$ as well as in the classical regime $\vartheta \to 0$ without imposing any step size restrictions. Moreover, the new schemes are asymptotic preserving and converge to the classical Zakharov system in the limit $\vartheta \to 0$ uniformly in the time discretization parameter. Numerical experiments underline the favorable error behavior of the new schemes with first- and second-order time convergence uniformly in $\vartheta$, first-order asymptotic convergence in $\vartheta$ and long time structure preservation properties.