Integration of the negative order Korteweg–de Vries equation with a self-consistent source in the class of periodic functions

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