Exact solution for many-body Hamiltonian of interacting particles with linear spectrum

The exact solution of the Schrödinger equation for the one-dimensional system of interacting particles with linear dispersion law in an arbitrary external field is found. The solution is reduced to two groups of particles moving with constant velocities in the opposite directions with a fixed distance between the particles in each group. The problem is applied to the edge states of the 2D topological insulator.