Abstract <p> We find the spectral data for Dirac’s operator with periodic potential that is connectedwith solution of the negative order Schrödinger equation with a self-consistent integralsource. We use the method of inverse spectral problems and study the question on completeintegration of the nonlinear negative order Schrödinger equation with a self-consistentintegral source in the class of periodic functions. We prove that there exists a solution ofthe Cauchy problem for the infinite Dubrovin–Trubowitz system of differential equations inthe class of three times continuously differentiable periodic functions. We obtain importantcorollaries on analytic properties and the period of a solution with respect to the spatial variable.</p>