Infinitesimal symmetries and conservation laws of the DNLSE hierarchy and the Noether's theorem

摘要

The hierarchy of the integrable nonlinear equations associated with thequadratic bundle is considered. The expressions for the solution of thelinearization of these equations and their conservation law in the terms of thesolutions of the corresponding Lax pairs are found. It is shown for the firstmember of the hierarchy that the conservation law is connected with thesolution of the linearized equation due to the Noether's theorem. The localhierarchy and three nonlocal ones of the infinitesimal symmetries and theconservation laws that are explicitly expressed through the variables of thenonlinear equations are derived.