There are several ways to prevent a wave from scattering.

The oldest known one is making the potential smooth, which protects conductance quantization in a quantum point contact. Topology of a gapped bulk of a quantum Hall insulator makes all the modes turn in the same direction and prevents them from scattering by separating them in space.

I am going to demonstrate how adiabaticity - the smoothness of the wave function evolution can be used to protect perfect transmission without relying on spatial separation. This effect of chiral adiabatic transmission appears in ballistic multiterminal Josephson junctions, and the number of chiral channels equals to the number of 2D Fermi surfaces of the normal state dispersion.

I will explain how both the propagation of the modes in a Josephson junction and their protection from scattering into each other are enabled by the same physical parameter - the curvature of the dispersion relation.