We compare three different ways of checking the Jacobi identity for weakly nonlocal Poisson brackets using the theory of distributions, of pseudodifferential operators and of Poisson vertex algebras, respectively. We show that the three approaches lead to similar computations and same results.

中文翻译：

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弱非局部泊松括号的三种计算方法

我们分别使用分布理论、伪微分算子和泊松顶点代数来比较三种不同的方法来检查弱非局部泊松括号的雅可比恒等式。我们表明这三种方法导致相似的计算和相同的结果。