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.
| Original language | English |
|---|---|
| Pages (from-to) | 377-400 |
| Number of pages | 24 |
| Journal | Journal of Nonlinear Mathematical Physics |
| Volume | 18 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1 Sept 2011 |
Keywords
- KdV in 2+1 dimensions
- Novikov-Veselov equation
- Transparent potentials
- large time asymptotics