Riemann--Hilbert problem approach for two-dimensional flow inverse scattering

Alexey Agaltsov (1) , Roman Novikov (2)

1 Lomonosov Moscow State University - Faculty of Computational Mathematics and Cybernetics
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann--Hilbert problem approach. Comparisons with preceding results are given.

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Alexey Agaltsov, Roman Novikov. Riemann--Hilbert problem approach for two-dimensional flow inverse scattering. Journal of Mathematical Physics, 2014, 55 (10), pp.103502. ⟨hal-00939283⟩