This occur when two phonons interact and the sum of their momenta add to a new wavevector outside the new Brillioun zone. The resulting wavevector is then mapped back into the Brillioun zone by subtraction of a suitable reciprocal lattice vector. I don't think I understand the physics in all of this. I understand the idea but what is physically going on in this process and where does the leftover momentum go?
The left over energy absorbed by the crystal; the momentum is not "real momentum" - it is crystal momentum, which is not conserved. See https://www.physicsforums.com/showthread.php?t=715639