An application of the inverse scattering problem for the discrete Dirac operator

The method of the inverse scattering problem is used to solve the Cauchy problem for the Langmuir lattice with initial data of step type. Formulas are obtained for transforming the scattering data with respect to the time, making it possible to obtain a... More

The method of the inverse scattering problem is used to solve the Cauchy problem for the Langmuir lattice with initial data of step type. Formulas are obtained for transforming the scattering data with respect to the time, making it possible to obtain a solution of the problem for arbitrary moment with the aid of linear integral equations of scattering theory. The existence of a solution is proved. Less