Integrable dispersive chains and energy dependent Schrödinger operator (Q2874763)

In this article the linear Schrödinger equation \(\psi_{xx}=u\psi\), \(u=u(x, t, \lambda)\) is in vestigated, where \(\lambda\) is a spectral parameter. The author considers some general properties of integrable dispersive chains as higher commuting flows, conservation laws and local Hamiltonian structures. In the article new dispersive integrable systems are constructed. The author finds explicit differential constraints and a reduction of these quasi-linear equations to dispersive integrable systems is made.