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Deconvolutional determination of the nonlinearity in a semilinear wave equation

Nicholas Hu, Rowan Killip and Monica Vişan
Vol. 7 (2025), No. 1, 1–17
DOI: 10.2140/paa.2025.7.1
Abstract

We demonstrate that in three space dimensions, the scattering behaviour of semilinear wave equations with quintic-type nonlinearities uniquely determines the nonlinearity. The nonlinearity is permitted to depend on both space and time.

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Keywords
dispersive equations, nonlinear wave equation, semilinear wave equation, scattering, inverse scattering, deconvolution
Mathematical Subject Classification
Primary: 35L70, 35P25, 35R30
Milestones
Received: 7 August 2023
Revised: 13 November 2024
Accepted: 31 December 2024
Published: 22 January 2025
Authors
Nicholas Hu
Department of Mathematics
University of California
Los Angeles, CA
United States
Rowan Killip
Department of Mathematics
University of California
Los Angeles, CA
United States
Monica Vişan
Department of Mathematics
University of California
Los Angeles, CA
United States
© 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers).