论文标题
Zakharov-Rubenchik方程的任意高阶能源保护方案
Arbitrarily high-order energy-preserving schemes for the Zakharov-Rubenchik equation
论文作者
论文摘要
在本文中，我们提出了一类新型的高阶能量保护方案，用于解决Zakharov-Rubenchik方程。该方案的主要思想首先引入了二次辅助变量，以将哈密顿能量转换为修改的二次能量，然后将原始系统重新构建为满足质量，修改的能量以及两个线性不变性的等效系统。及时的符合性runge-kutta方法与空间中的傅立叶伪谱法一起用于计算重新制度的解决方案。提出的方案的主要好处是，它可以随时间获得任意高阶精度并保存三个不变性：质量，汉密尔顿能量和两个线性不变性。另外，提出了有效的定点迭代，以求解所提出的方案的产生的非线性方程。解决了几个实验以验证理论结果。
In this paper, we present a novel class of high-order energy-preserving schemes for solving the Zakharov-Rubenchik equations. The main idea of the scheme is first to introduce an quadratic auxiliary variable to transform the Hamiltonian energy into a modified quadratic energy and the original system is then reformulated into an equivalent system which satisfies the mass, modified energy as well as two linear invariants. The symplectic Runge-Kutta method in time, together with the Fourier pseudo-spectral method in space is employed to compute the solution of the reformulated system. The main benefit of the proposed schemes is that it can achieve arbitrarily high-order accurate in time and conserve the three invariants: mass, Hamiltonian energy and two linear invariants. In addition, an efficient fixed-point iteration is proposed to solve the resulting nonlinear equations of the proposed schemes. Several experiments are addressed to validate the theoretical results.
