One dimensional gas of bosons with integrable resonant interactions

We develop an exact solution to the problem of one dimensional chiral bosons interacting via an s-wave Feshbach resonance. This problem is integrable, being the quantum analog of a classical two-wave model solved by the inverse scattering method thirty years ago. Its solution describes one or two branches of dressed chiral right moving molecules depending on the chemical potential (particle density). We also briefly discuss the possibility of experimental realization of such a system.