The derivation of conservation laws for nonlinear Schroedinger equations with a power type nonlinearity

TL;DR

This paper introduces a new, simplified method to derive conservation laws for nonlinear Schrödinger equations with power nonlinearities, avoiding approximation procedures and enhancing theoretical understanding.

Contribution

A novel approach that simplifies deriving conservation laws for nonlinear Schrödinger equations without using approximations.

Findings

Derived conservation laws for momentum and pseudo conformal symmetry

Simplified derivation process without approximations

Enhanced theoretical framework for nonlinear Schrödinger equations

Abstract

For nonlinear Schroedinger equations with a power nonlinearity, a new approach to derive the conservation law of the momentum and the pseudo conformal conservation law is obtained. Since this approach does not contain approximating procedure, the argument is simplified to derive these conservation laws.