|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
Sobolev norms of
$L^2$-solutions to the nonlinear Schrödinger equation
Roman V. Bessonov and Sergey A. Denisov |
|
Vol. 331 (2024), No. 2, 217–258
|
 |
Abstract |
|
We apply inverse spectral theory to study Sobolev norms of solutions to the nonlinear Schrödinger equation. For initial datum and , we prove that there exists a conserved quantity which is equivalent to -norm of the solution. |
Keywords
Dirac operators, NLSE, scattering, Sobolev norms
|
Mathematical Subject Classification
Primary: 35Q55
|
Milestones
Received: 1 February 2024
Revised: 2 August 2024
Accepted: 14 September 2024
Published: 30 October 2024
|
Authors |
| Roman V. Bessonov | |
| St. Petersburg State
University St. Petersburg Russia |
St. Petersburg Department of Steklov
Mathematical Institute Russian Academy of Sciences St. Petersburg Russia |
| Sergey A. Denisov | |
| Department of Mathematics University of Wisconsin-Madison Madison, WI United States |
|
| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
