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

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

2010-10-14

arxiv.org/abs/1010.2897v1

Mathematics

Analysis of PDEs

Scientific paper

10.1142/S1402925111001660

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.

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