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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.
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
© 2025 The Author(s), under
exclusive license to MSP (Mathematical Sciences
Publishers).