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| HAL: hal-00606501, version 2 |
| arXiv: 1107.1150 |
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| Available versions: | v1 (2011-07-06) | v2 (2011-10-04) |
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| A large time asymptotics for the solution of the Cauchy problem for the Novikov-Veselov equation at negative energy with non-singular scattering data |
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| Anna Kazeykina 1 |
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| (2011-07-06) |
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| In the present paper we are concerned with the Novikov--Veselov equation at negative energy, i.e. with the $ ( 2 + 1 ) $--dimensional analog of the KdV equation integrable by the method of inverse scattering for the two--dimensional Schrödinger equation at negative energy. We show that the solution of the Cauchy problem for this equation with non--singular scattering data behaves asymptotically as $ \frac{ \const }{ t^{ 3/4 } } $ in the uniform norm at large times $ t $. We also present some arguments which indicate that this asymptotics is optimal. |
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| 1: | Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP) |
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Polytechnique - X – CNRS : UMR7641 |
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| Subject | : | Mathematics/Analysis of PDEs Mathematics/Mathematical Physics Physics/Mathematical Physics |
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| hal-00606501, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00606501 | |
| oai:hal.archives-ouvertes.fr:hal-00606501 | |
| From: Anna Kazeykina | |
| Submitted on: Tuesday, 4 October 2011 14:24:57 | |
| Updated on: Tuesday, 4 October 2011 21:01:41 | |
