A large time asymptotics for transparent potentials for the Novikov-Veselov equation at positive energy

Anna Kazeykina (1) , Roman Novikov (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

In the present paper we begin studies on the large time asymptotic behavior for solutions of the Cauchy problem for the Novikov--Veselov equation (an analog of KdV in 2 + 1 dimensions) at positive energy. In addition, we are focused on a family of reflectionless (transparent) potentials parameterized by a function of two variables. In particular, we show that there are no isolated soliton type waves in the large time asymptotics for these solutions in contrast with well-known large time asymptotics for solutions of the KdV equation with reflectionless initial data.

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

Anna Kazeykina, Roman Novikov. A large time asymptotics for transparent potentials for the Novikov-Veselov equation at positive energy. Journal of Nonlinear Mathematical Physics, 2011, 18 (3), pp.377-400. ⟨10.1142/S1402925111001660⟩. ⟨hal-00526400⟩