Deconvolutional determination of the nonlinearity in a semilinear wave equation
Nicholas Hu, Rowan Killip, Monica Visan
TL;DR
This paper shows that in three dimensions, the scattering behavior of semilinear wave equations with space- and time-dependent quintic nonlinearities uniquely identifies the nonlinearity, advancing understanding of inverse problems in wave equations.
Contribution
It establishes a uniqueness result for determining the nonlinearity in semilinear wave equations from scattering data in three dimensions.
Findings
Scattering behavior uniquely determines the nonlinearity.
Nonlinearity can depend on space and time.
Results apply to quintic-type nonlinearities.
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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Taxonomy
TopicsNonlinear Photonic Systems · Advanced Mathematical Physics Problems · Advanced Fiber Laser Technologies