Download this article
Download this article For screen
For printing
Recent Issues
Volume 6, Issue 4
Volume 6, Issue 3
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN 2578-5885 (online)
ISSN 2578-5893 (print)
Author Index
To Appear
 
Other MSP Journals
Inverse scattering for critical semilinear wave equations

Antônio Sá Barreto, Gunther Uhlmann and Yiran Wang
Vol. 4 (2022), No. 2, 191–223
DOI: 10.2140/paa.2022.4.191
Abstract

We show that the scattering operator for defocusing energy critical semilinear wave equations □u + f(u) = 0, f ∈ C∞(ℝ) and f ∼ u5, in three space dimensions, determines f.

Keywords
nonlinear wave equations, radiation fields, scattering, inverse scattering
Mathematical Subject Classification
Primary: 35P25, 58J50, 35R30
Milestones
Received: 19 January 2021
Accepted: 5 January 2022
Published: 16 October 2022
Authors
Antônio Sá Barreto
Department of Mathematics
Purdue University
West Lafayette, IN
United States
Gunther Uhlmann
Department of Mathematics
University of Washington
Seattle, WA
United States		 Institute for Advanced Study
Hong Kong University of Science and Technology
Clear Water Bay
Hong Kong
Yiran Wang
Department of Mathematics
Emory University
Atlanta, GA
United States