Integrable nonlinear lattice associated with the  third-order spectral problem

Abstract:
We propose a nonlinear model on a regular infinite one-dimensional lattice. It describes the three component dynamical system with modulated on-site masses and is shown to admit a zero-curvature representation. The associated auxiliary spectral problem is basically of  third order and gives rise to fairly complicated subdivision
into domains of regularity of Jost functions in the plane of complex spectral parameter. As a result, both the direct and the inverse scattering problems turn out to be
substantially nontrivial. The Caudrey version of the direct and inverse scattering technique for the needs of model integration is adapted. The simplest soliton solution is found.