In this paper, based on the paradigm of supplementary variable method (SVM), we reformulate the Klein–Gordon–Zakharov system into equivalent optimization problem subject to PDE constraints, and then present a novel class of high-order energy-preserving numerical algorithms to solve it numerically. The optimization model is discretized by applying the Gauss collocation method as well as the prediction–correction technique in time and the sine pseudo-spectral method in space. Experimental results and some comparisons between this method and other reported ones are provided to favor the suggested method in the overall performance.

中文翻译：

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Klein-Gordon-Zakharov 系统的一类新的高阶补充变量方法


在本文中，基于补充变量方法（SVM）范式，我们将Klein-Gordon-Zakharov系统重新表述为受偏微分方程约束的等价优化问题，然后提出一类新颖的高阶能量守恒数值算法用数值方法解决它。采用高斯配置法以及时间上的预测校正技术和空间上的正弦伪谱方法对优化模型进行离散化。提供了实验结果以及该方法与其他报道方法之间的一些比较，以支持建议方法的整体性能。