Integration of the Loaded Negative Order Korteweg-De Vries Equation in the Class of Periodic Functions

Abstract

In this paper, we consider the loaded Korteweg-de Vries equation of negative order in the class of periodic functions corresponding to the eigenvalues of the corresponding spectral problem. It is shown that the considered equation 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 the considered equation is determined. The obtained results make it possible to apply the inverse problem method for solving the loaded Korteweg-de Vries equation of negative order in the class of periodic functions corresponding to the eigenvalues of the corresponding spectral problem.