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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.16691 |
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| _version_ | 1866911690796302336 |
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| author | Machihara, Shuji Miyazaki, Hayato Ozawa, Tohru |
| author_facet | Machihara, Shuji Miyazaki, Hayato Ozawa, Tohru |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16691 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Unified Integral Equation Approach to Conservation Laws for Nonlinear Schrödinger Equations Machihara, Shuji Miyazaki, Hayato Ozawa, Tohru Analysis of PDEs 35Q55, 37K06 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. |
| title | A Unified Integral Equation Approach to Conservation Laws for Nonlinear Schrödinger Equations |
| topic | Analysis of PDEs 35Q55, 37K06 |
| url | https://arxiv.org/abs/2605.16691 |