On the Integration of the Higher Order Toda Lattice with a Self-Consistent Integral Type Source (Contemporary Mathematics, 2023)
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.
Keywords: higher Toda lattice; self-consistent source; inverse scattering method; discrete Sturm-Liouville operator; one-soliton solution