4.7 Article

Weakly nonlocal Poisson brackets: Tools, examples, computations

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Summary: The paper demonstrates that in low dimensions, the WDVV equations are bi-Hamiltonian and proves the invariance of bi-Hamiltonian formalism for N = 3. Further examples in higher dimensions suggest that this result may hold in general. The invariance group of the bi-Hamiltonian pairs found for WDVV equations is the group of projective transformations, and the significance of projective invariance is discussed in detail. The computer algebra programs used for calculations in the paper are provided in a GitHub repository.

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