Abstract
We investigate the vacuum $pp$-wave and Aichelburg-Sexl-type solutions in $f(R)$ and the modified Gauss-Bonnet theories of gravity with both minimal and nonminimal couplings between matter and geometry. In each case, we obtain the necessary condition for the theory to admit the solution and examine it for several specific models. We show that the wave profiles are the same or proportional to the general relativistic one.
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