Scattering theory for the loaded negative order Korteweg–de Vries equation

In this paper, we consider the loaded negative order Korteweg–de Vries equation. The evolution of the spectral data of the Sturm–Liouville operator with a potential associated with the solution of the loaded negative order Korteweg–de Vries equation is determined. The obtained results make it possible to apply the inverse problem method to solve the loaded negative order Korteweg–de Vries equation in the class of rapidly decreasing functions. An example of the given problem is given with graphs of the solution.