High-order schemes with mass and energy conservation for solving the one-dimensional Zakharov system

Abstract In this paper, we present high-order schemes to solve the Zakharov system (ZS) with periodic initial values. Semi-discrete schemes are capable of perfectly preserving the conservation of mass and energy. When we use the Crank-Nicolson (CN) method in time, we obtain full-discrete schemes that ensure the conservation of mass. Full-discrete schemes can achieve second-order accuracy in time and fourth-order and sixth-order accuracy in space. The presented numerical results aim to test accuracy order, examine conservation property, and simulate dynamic behavior.