A priori estimates for a quadratic dNLS
- Resource Type
- Working Paper
- Authors
- Klaus, Friedrich
- Source
- Subject
- Mathematics - Analysis of PDEs
35Q55 (Primary), 37K10 (Secondary)
- Language
In this work we consider integrable PDE with higher dimensional Lax pairs. Our main example is a quadratic dNLS equation with a $3 \times 3$ Lax pair. For this equation we show a-priori estimates in Sobolev spaces of negative regularity $H^s(\mathbb{R}), s > -\frac{1}{2}$. We also prove that for general $N \times N$ Lax operators $L$, the transmission coefficient coincides with the $2$-renormalized perturbation determinant.
Comment: 26 pages