We study exact impulsive gravitational waves propagating in anti-de Sitter spacetime in the context of the ghost-free infinite derivative gravity. We show that the source-free theory does not admit any anti-de Sitter wave solutions other than that of Einstein's general relativity. The situation is significantly different in the presence of sources. We construct impulsive-wave solutions of the infinite derivative gravity generated by massless particles and linear sources in four and three dimensions. The singularities corresponding to distributional curvature at the locations of the sources get smeared by the nonlocalities. The obtained solutions are regular everywhere. They reduce to the corresponding solutions of general relativity in the infrared regime and in the local limit.

We study solutions describing spinning null sources called gyratons in generic theories of gravity with terms that are quadratic in curvature and contain an arbitrary number of covariant derivatives. In particular, we show that the properties of pp waves of the algebraic type III allow for extreme simplification of the field equations. It turns out that the resulting differential equations are exactly solvable due to partial decoupling and linearity of the equations. This is demonstrated explicitly by finding axially symmetric gyraton solutions in Stelle's fourth derivative gravity and the nonlocal gravity with an infinite number of derivatives.

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