6533b860fe1ef96bd12c3c51
RESEARCH PRODUCT
The fixed angle scattering problem with a first order perturbation
Mikko SaloCristóbal J. MeroñoLeyter Potenciano-machadosubject
PhysicsNuclear and High Energy Physicsinverse scattering problemsScattering010102 general mathematicsMathematical analysisPlane waveInverseFOS: Physical sciencesStatistical and Nonlinear PhysicsMathematical Physics (math-ph)Gauge (firearms)Wave equation01 natural sciencesinversio-ongelmat010101 applied mathematicsMathematics - Analysis of PDEsInverse scattering problemFOS: MathematicsGauge theoryElectric potential0101 mathematicsMathematical PhysicsAnalysis of PDEs (math.AP)description
We study the inverse scattering problem of determining a magnetic field and electric potential from scattering measurements corresponding to finitely many plane waves. The main result shows that the coefficients are uniquely determined by $2n$ measurements up to a natural gauge. We also show that one can recover the full first order term for a related equation having no gauge invariance, and that it is possible to reduce the number of measurements if the coefficients have certain symmetries. This work extends the fixed angle scattering results of Rakesh and M. Salo to Hamiltonians with first order perturbations, and it is based on wave equation methods and Carleman estimates.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-01-01 |