In this paper, we present a new methodology to develop arbitrary high-order structure-preserving methods for solving the quantum Zakharov system. The key ingredients of our method are: (i) the original Hamiltonian energy is reformulated into a quadratic form by introducing a new quadratic auxiliary variable; (ii) based on the energy variational principle, the original system is then rewritten into a new equivalent system which inherits the mass conservation law and a quadratic energy; (iii) the resulting system is discretized by symplectic Runge-Kutta method in time combining with the Fourier pseudo-spectral method in space. The proposed method achieves arbitrary high-order accurate in time and can preserve the discrete mass and original Hamiltonian energy exactly. Moreover, an efficient iterative solver is presented to solve the resulting discrete nonlinear equations. Finally, ample numerical examples are presented to demonstrate the theoretical claims and illustrate the efficiency of our methods.

翻译：本文提出了一种构建任意高阶保结构方法的新框架，用于求解量子Zakharov系统。该方法的核心要素包括：(i) 通过引入新型二次辅助变量，将原始哈密顿能量重构为二次形式；(ii) 基于能量变分原理，将原始系统重新表述为保持质量守恒律与二次能量的等价新系统；(iii) 对该系统采用时间方向上的辛Runge-Kutta方法结合空间方向上的傅里叶拟谱方法进行离散。所提方法在时间维度上可实现任意高阶精度，并精确保持离散质量与原始哈密顿能量。此外，本文还设计了一种高效迭代求解器用于处理离散非线性方程组。最后通过大量数值算例验证了理论分析结果并展示了方法的计算效率。