The Canonical Symmetry and Hamiltonian Formalism. I. Conservation Laws

TL;DR

This paper investigates the canonical symmetry of the nonlinear Schrödinger equation, showing how conservation law densities transform under this symmetry through total derivatives, contributing to the understanding of symmetries in Hamiltonian systems.

Contribution

It introduces a detailed analysis of how canonical symmetry affects conservation laws in the nonlinear Schrödinger equation within the Hamiltonian formalism.

Findings

Conservation law densities change by total derivatives under canonical symmetry.

The properties of the canonical symmetry are characterized in the Hamiltonian framework.

The results deepen understanding of symmetry transformations in nonlinear integrable systems.

Abstract

The properties of the canonical symmetry of the nonlinear Schr\"odinger equation are investigated. The densities of the local conservation laws for this system are shown to change under the action of the canonical symmetry by total space derivatives.