Trace formulas revisited and a new representation of KdV solutions with short-range initial data
Mathematical Physics
2024-09-30 v2 Analysis of PDEs
math.MP
Abstract
We put forward a new approach to Deift-Trubowitz type trace formulas for the 1D Schrodinger operator with potentials that are summable with the first moment (short-range potentials). We prove that these formulas are preserved under the KdV flow whereas the class of short-range potentials is not. Finally, we show that our formulas are well-suited to study the dispersive smoothing effect.
Keywords
Cite
@article{arxiv.2308.13656,
title = {Trace formulas revisited and a new representation of KdV solutions with short-range initial data},
author = {Alexei Rybkin},
journal= {arXiv preprint arXiv:2308.13656},
year = {2024}
}
Comments
To appear in Nonlinearity