Integrable dispersive chains and energy dependent Schrödinger operator

In this paper we consider integrable dispersive chains associated with the so-called ‘energy dependent’ Schrödinger operator. In a general case multi-component reductions of these dispersive chains are new integrable systems, which are characterized by two arbitrary natural numbers. Also we show that integrable three-dimensional linearly degenerate quasilinear equations of a second order possess infinitely many differential constraints. Corresponding dispersive reductions are integrable systems associated with the ‘energy dependent’ Schrödinger operator.