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By performing numerical simulations, we discuss the collisional dynamics ofstable solitary waves in the Schrodinger-Poisson equation. In the framework ofa model in which part or all of dark matter is a Bose-Einstein condensate ofultralight axions, we show that these dynamics can naturally account for therelative displacement between dark and ordinary matter in the galactic clusterAbell 3827, whose recent observation is the first empirical evidence of darkmatter interactions beyond gravity. The essential assumption is the existenceof solitonic galactic cores in the kiloparsec scale. For this reason, wepresent simulations with a benchmark value of the axion mass $m_a = 2 \times10^{-24}$ eV, which is somewhat lower than the one preferred for cosmologicalstructure formation if the field is all of dark matter ($m_a \approx10^{-22}$eV). We argue that future observations might bear out or falsify thiscoherent wave interpretation of dark matter offsets.

Interference of Dark Matter Solitons and Galactic Offsets