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

One dimensional gas of bosons with integrable resonant interactions