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arXiv · 1107.1150

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
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Abstract

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.

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Anna Kazeykina. 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. https://doi.org/10.1088/0266-5611%2F28%2F5%2F055017

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