Публикации автора

We show that the inverse scattering transform technique can be applied to obtain the time dependence of scattering data of the Zakharov — Shabat system, which is described by the loaded nonlinear Schr ̈odinger equation in the class of fast decaying functions. In addition we prove that the Cauchy problem for the loaded nonlinear Schr ̈odinger equation is uniquely solvable in the class of rapidly decreasing functions. We provide the explicit expression of a single soliton solution for the loaded nonlinear Schr ̈odinger equation. As an example, we find the soliton solution of the considered problem for an arbitrary non–zero continuous function