Integrable Nonlinear Equations (Discrete Case)
The method of the inverse scattering problems is widely used when analysing nonlinear continuous and discrete systems , , Yu.M.Beresanskii started using the method of the inverse spectral problem for the investigation of the nonlinear discrete systems . A number of works on the application of the method of the inverse spectral problem both to discrete and continuous systems belongs to the author of this book , . In this chapter the results refferring to the discrete case are stated. The evolution law of spectral data is deduced here, the hierarchy of the equations is constructed. When N = 1 the member of the hierarchy coincides with the To da equation, when N = 2 the member of the hierarchy coincides with the Volterra equation.
Unable to display preview. Download preview PDF.