On periodic solutions of the negative-order Schrodinger equation with an integral-type self-consistent source

In the present work, the spectral data of the Dirac operator with a periodic potential associated with the solution of a negative-order Schrodinger equation with an integral-type self-consistent source are obtained. Using the inverse spectral method, the complete integrability of the negative-order nonlinear Schrodinger equation with an integral-type self-consistent source is investigated in the class of periodic functions. The solvability of the Cauchy problem for the infinite Dubrovin–Trubowitz system of differential equations is proved in the class of thrice continuously differentiable periodic functions. Important results are obtained concerning the analyticity and spatial periodicity of the solution.

УДК 517.957

Keywords: negative-order nonlinear Schrodinger equation, integral-type source, Dirac operator, inverse spectral problem, trace formulas.