论文标题
Quantum Zakharov系统的任意高级结构保留方法
Arbitrary high-order structure-preserving methods for the quantum Zakharov system
论文作者
论文摘要
在本文中，我们提出了一种新的方法，用于开发任意的高阶结构延伸方法来解决量子Zakharov系统。我们方法的关键要素是：（i）通过引入新的二次辅助变量，将原始的汉密尔顿能量重新制定为二次形式； （ii）基于能量变异原理，然后将原始系统重写为一个新的等效系统，该系统继承了大众保护法和二次能量； （iii）所得系统通过及时与空间中的傅立叶伪 - 光谱法相结合，通过符号runge-kutta方法离散。所提出的方法可以在时间上达到任意高阶精度，并可以准确地保留离散的质量和原始的哈密顿能量。此外，提出了有效的迭代求解器来求解所得的离散非线性方程。最后，提出了足够的数值示例，以证明理论主张并说明了我们方法的效率。
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.
