Integration of the KdV equation of negative order with a free term in the class of periodic functions

In this paper, we consider the KdV equation of negative order with a free term in the class of periodic functions. It is shown that the KdV equation of negative order with a free term in the class of periodic functions can be integrated by the method of the inverse spectral problem. The evolution of the spectral data of the Sturm–Liouville operator with a periodic potential associated with the solution of a negative-order KdV equation with a free term in the class of periodic functions is determined. The results obtained make it possible to apply the inverse problem method to the solution of the KdV equation of negative order with a free term in the class of periodic functions.