The modified Novikov-Veslov Equation and the Inverse Scattering Transform
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917103941976064 |
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| author | Perry, Peter A. |
| author_facet | Perry, Peter A. |
| contents | This paper corrects several errors in the author's previous papers (Journal of Spectral Theory 2016, Analysis and PDE 2014) on the Davey-Stewartson II (DS II) and modified Novikov-Veselov (mNV) equations. In each of these papers a proof was given that the solution by inverse scattering yields a classical solution to the PDE. The mNV equation lies in the integrable hierarchy of the DS II equation, so the same scattering transform may be used in both cases. In the 2014 paper, an incorrect formula is given for the nonlinearity in the mNV equation. Here we correct errors in the proof and obtain a correct statement of the mNV equation as solved by inverse scattering. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20579 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The modified Novikov-Veslov Equation and the Inverse Scattering Transform Perry, Peter A. Analysis of PDEs Primary 37K15, Secondary 35Q35 This paper corrects several errors in the author's previous papers (Journal of Spectral Theory 2016, Analysis and PDE 2014) on the Davey-Stewartson II (DS II) and modified Novikov-Veselov (mNV) equations. In each of these papers a proof was given that the solution by inverse scattering yields a classical solution to the PDE. The mNV equation lies in the integrable hierarchy of the DS II equation, so the same scattering transform may be used in both cases. In the 2014 paper, an incorrect formula is given for the nonlinearity in the mNV equation. Here we correct errors in the proof and obtain a correct statement of the mNV equation as solved by inverse scattering. |
| title | The modified Novikov-Veslov Equation and the Inverse Scattering Transform |
| topic | Analysis of PDEs Primary 37K15, Secondary 35Q35 |
| url | https://arxiv.org/abs/2511.20579 |