Integrable Dispersive Chains and Energy Dependent Schrodinger Operator

In this paper we consider integrable dispersive chains associated with the so called Energy Dependent Schrodinger operator. In a general case multi component reductions of these dispersive chains are new integrable systems, which are characterised 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 Schrodinger operator.