On the Integration of the Higher Order Toda Lattice with a Self-Consistent Integral Type Source

This work presents an algorithm that uses the inverse scattering method to find a solution for the higher-order Toda lattice with a self-consistent source. The higher-order Toda lattice with an integral-type source is also a significant theoretical model belonging to very integrable systems. The problem is solved by applying the direct and inverse scattering methods to the discrete Sturm-Liouville operator, and the time dependence of the scattering data for this operator is attained. The solution to the problem is set up using the inverse scattering transform (IST) approach.