In this paper, we present a high-order energy-preserving scheme for solving Zakharov-Rubenchik equation. The main idea of the method is first to reformulate the original system into an equivalent one by introducing an quadratic auxiliary variable, and the symplectic Runge-Kutta method, together with the Fourier pseudo-spectral method is then employed to compute the solution of the reformulated system. The main benefit of the proposed method is that it can conserve the three invariants of the original system and achieves arbitrarily high-order accurate in time. In addition, an efficient fixed-point iteration is proposed to solve the resulting nonlinear equations of the proposed schemes. Several experiments are provided to validate the theoretical results.

翻译：在本文中,我们提出了一个解决Zakharov-Rubenchik等式的高序节能计划,该方法的主要想法是首先通过引入二次辅助变量,将原系统改造成等效系统,然后采用静电龙格-库塔法以及四重伪光谱法来计算重订系统的解决办法,拟议方法的主要好处是,它能够保护原系统的三种变异,并实现任意高序准确性。此外,还提出了高效的固定点迭代,以解决所拟方案所产生的非线性方程式。为验证理论结果,提供了若干实验。