Geometric structure of NLS evolution

TL;DR

This paper explores the geometric structure of the nonlinear Schrödinger equation, connecting Hamiltonian and Lagrangian frameworks, and elucidates the least action principle and Noether theorem within this context.

Contribution

It clarifies the geometric relationship between Hamiltonian and Lagrangian approaches for NLS and explains fundamental principles like least action and Noether theorem.

Findings

Unified geometric perspective of NLS evolution

Explicit connection between Hamiltonian and Lagrangian formalisms

Insight into symmetry principles via Noether's theorem

Abstract

We clarify the relation between the Hamiltonian and Lagrangian approaches to nonlinear evolution equations, focusing specifically on the nonlinear Schroedinger equation. In particular, we explain the least action principle and the Noether theorem in this context.