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arXiv · 2605.16691

A Unified Integral Equation Approach to Conservation Laws for Nonlinear Schrödinger Equations

Shuji Machihara·Hayato Miyazaki·Tohru Ozawa
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Abstract

We present a unified framework for the rigorous derivation of conservation laws and related identities for nonlinear Schrödinger equations with power-type nonlinearities. This approach treats the equation in its Duhamel form and uses the space-time integrability provided by Strichartz estimates, without relying on smooth approximations or regularization procedures. It was first introduced by the third author in [20] and subsequently developed in [7, 13]. In this paper, we establish a single integral identity from which all of the laws and identities considered here follow systematically. These include the conservation of charge (mass), energy, and momentum, the pseudo-conformal conservation law, and virial-type identities.

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Shuji Machihara, Hayato Miyazaki, Tohru Ozawa. 2026-06-22. A Unified Integral Equation Approach to Conservation Laws for Nonlinear Schrödinger Equations. https://arxiv.org/abs/2605.16691

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