Work

Trace formulas revisited and a new representation of KdV solutions with short-range initial data

Year: 2024

Type: article

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.

Source: Nonlinearity

DOI: 10.1088/1361-6544/ad7c10

Author: Alexei Rybkin

Institution: University of Alaska Fairbanks

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Integrable PDEs beyond standard assumptions on initial data