Infinitesimal symmetries and conservation laws of the DNLSE hierarchy and the Noether's theorem
Quantum Field Theory Department, Tomsk State University, 634050 Tomsk, Russia
Corresponding author: a email@example.com
Revised: 9 July 2007
Published online: 8 September 2007
The hierarchy of integrable nonlinear equations associated with the quadratic bundle is considered. The expressions for the solution of linearization of these equations and their conservation law in the terms of solutions of corresponding Lax pairs are found. It is shown for the first member of the hierarchy that the conservation law is connected with the solution of linearized equation due to the Noether's theorem. The local hierarchy and three nonlocal ones of the infinitesimal symmetries and conservation laws explicitly expressed through the variables of the nonlinear equations are derived.
PACS: 02.30.Jr – Partial differential equations / 05.45.Yv – Solitons
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007