A large time asymptotics for the solution of the Cauchy problem for the Novikov-Veselov equation at negative energy with non-singular scattering data

Anna Kazeykina (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

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.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Anna Kazeykina. 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. ⟨hal-00606501v2⟩