English

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