We demonstrate, through numerical simulations, the emission of a coherent continuous matter wave of constant amplitude from a Bose–Einstein condensate in a shallow optical dipole trap. The process is achieved by spatial control of the variations of the scattering length along the trapping axis, including elastic three-body interactions due to dipole interactions. In our approach, the outcoupling mechanism is atomic interactions, and thus, the trap remains unaltered. We calculate analytically the parameters for the experimental implementation of this continuous wave atom laser