Large time asymptotics for the Grinevich-Zakharov potentials

Anna Kazeykina (1) , Roman Novikov (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

In this article we show that the large time asymptotics for the Grinevich-Zakharov rational solutions of the Novikov-Veselov equation at positive energy (an analog of KdV in 2+1 dimensions) is given by a finite sum of localized travel waves (solitons).

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

Anna Kazeykina, Roman Novikov. Large time asymptotics for the Grinevich-Zakharov potentials. Bulletin des Sciences Mathématiques, 2011, 135 (4), pp.374-382. ⟨10.1016/j.bulsci.2011.02.003⟩. ⟨hal-00536791v2⟩