This paper introduces a new symbolic-numeric strategy for finding semidiscretizations of a given PDE that preserve multiple local conservation laws. We prove that for one spatial dimension, various one-step time integrators from the literature preserve fully discrete local conservation laws whose densities are either quadratic or a Hamiltonian. The approach generalizes to time integrators with more steps and conservation laws of other kinds; higher-dimensional PDEs can be treated by iterating the new strategy. We use the Boussinesq equation as a benchmark and introduce new families of schemes of order two and four that preserve three conservation laws. We show that the new technique is practicable for PDEs with three dependent variables, introducing as an example new families of second-order schemes for the potential Kadomtsev-Petviashvili equation.

翻译：本文引入了一种新的象征性数字战略,以寻找维护多种地方养护法的PDE的半分化。我们证明,对于一个空间层面,文献中各一步时间融合者保留了完全独立的当地养护法,其密度要么是二次变数,要么是汉密尔顿人。这一方法概括了时间融合者,增加了其他类型的步骤和养护法;高维度的PDE可以通过对新战略进行循环处理。我们用Boussinesq等式作为基准,并引入了维护三项养护法的第二、四级新顺序组合。我们表明,新技术对于具有三个依赖变量的PDEs来说是可行的,我们举例介绍了潜在的Kadomotsev-Petviashvili等式二等式二等式新组合。