Asymptotic Consistent Formulation and Numerical Methods for the Periodic Zakharov System in the Subsonic Limit Regime

Abstract. In this work, we analyze the asymptotic consistent formulation (ACF) for the periodic Zakharov system (ZS) in the subsonic limit, where the dimensionless parameter [Formula: see text] approaches zero, signifying an increase in acoustic speed. The primary focus is to determine the optimal asymptotic order of the functions involved in the ACF as [Formula: see text] for various types of initial data. A high-order extension of the ACF is proposed. Additionally, multiscale integrators based on the ACF are proposed, and their uniform accuracy and asymptotic-preserving properties are discussed. Numerical experiments are conducted to illustrate the performance of these schemes and explore the convergence of the ZS in the subsonic limit. To the best of our knowledge, this is the first time that the asymptotic behavior of the periodic ZS has been rigorously analyzed. Our results show that the behavior of the periodic ZS in the subsonic limit is different from that of the ZS in the whole space.