Volume 18, Issue 3, September 2011, Pages 377 - 400
A Large Time Asymptotics for Transparent Potentials for the Novikov–Veselov Equation at Positive Energy
Authors
A. V. Kazeykina
Centre des Mathématiques Appliquées, Ecole Polytechnique, Palaiseau, 91128, France
Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow, 119991, Russia,kazeykina@cmap.polytechnique.fr
R. G. Novikov
CNRS (UMR 7641), Centre des Mathématiques Appliquées, Ecole Polytechnique, Palaiseau, 91128, France
International Institute of Earthquake Prediction, Theory and Mathematical Geophysics, Russian Academy of Sciences, Profsoyuznaya str., 84/32, Moscow, 117997, Russia,novikov@cmap.polytechnique.fr
Received 14 October 2010, Accepted 9 February 2011, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925111001660How to use a DOI?
- Keywords
- Transparent potentials; Novikov–Veselov equation; KdV in 2+1 dimensions; large time asymptotics
- Abstract
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.
- Copyright
- © 2011 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - A. V. Kazeykina AU - R. G. Novikov PY - 2021 DA - 2021/01/07 TI - A Large Time Asymptotics for Transparent Potentials for the Novikov–Veselov Equation at Positive Energy JO - Journal of Nonlinear Mathematical Physics SP - 377 EP - 400 VL - 18 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925111001660 DO - 10.1142/S1402925111001660 ID - Kazeykina2021 ER -