21778 articles – 15587 references  [version française]
 HAL: hal-00606501, version 2
 arXiv: 1107.1150
 Available versions: v1 (2011-07-06) v2 (2011-10-04)
 A large time asymptotics for the solution of the Cauchy problem for the Novikov-Veselov equation at negative energy with non-singular scattering data
 (2011-07-06)
 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.
 1: Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP) Polytechnique - X – CNRS : UMR7641
 Subject : Mathematics/Analysis of PDEsMathematics/Mathematical PhysicsPhysics/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