  We construct supersymmetric solutions of $D=11$ supergravity, preserving 1/4
of the supersymmetry, that are holographically dual to ABJM theory which has
been deformed by spatially varying mass terms depending on one of the two
spatial directions. We show that the BPS equations reduce to the Helmholtz
equation on the complex plane leading to rich classes of new solutions. In
particular, the construction gives rise to infinite classes of supersymmetric
boomerang RG flows, as well as generalising a known Janus solution.
