A numerical solution to the Zakharov-Shabat inverse scattering problem with application to solitary wave propagation in nonlinear optical fibers

1996 ◽  
Vol 123 (4-6) ◽  
pp. 743-751 ◽  
Author(s):  
P. Frangos
Keyword(s):  
Wave Propagation ◽  
Solitary Wave ◽  
Numerical Solution ◽  
Inverse Scattering ◽  
Optical Fibers ◽  
Nonlinear Optical ◽  
Scattering Problem ◽  
Inverse Scattering Problem

scholarly journals Regularization and numerical solution of the inverse scattering problem using shearlet frames

2017 ◽  
Vol 25 (3) ◽  
Author(s):  
Gitta Kutyniok ◽  
Volker Mehrmann ◽  
Philipp C. Petersen
Keyword(s):  
Numerical Solution ◽  
Nonlinear Problem ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Scattering Problems ◽  
Algorithmic Approach ◽  
Linearized Problem ◽  
Regularization Techniques ◽  
Two Space Dimensions

AbstractRegularization techniques for the numerical solution of inverse scattering problems in two space dimensions are discussed. Assuming that the boundary of a scatterer is its most prominent feature, we exploit as model the class of cartoon-like functions. Since functions in this class are asymptotically optimally sparsely approximated by shearlet frames, we consider shearlets as a means for regularization. We analyze two approaches, namely solvers for the nonlinear problem and for the linearized problem obtained by the Born approximation. As example for the first class we study the acoustic inverse scattering problem, and for the second class, the inverse scattering problem of the Schrödinger equation. Whereas our emphasis for the linearized problem is more on the theoretical side due to the standardness of associated solvers, we provide numerical examples for the nonlinear problem that highlight the effectiveness of our algorithmic approach.

The Landweber Iteration for an Inverse Scattering Problem

1995 ◽  
Author(s):  
Martin Hanke ◽  
Frank Hettlich ◽  
Otmar Scherzer
Keyword(s):  
Numerical Solution ◽  
Inverse Scattering ◽  
Obstacle Problem ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Field Operator ◽  
Iteration Scheme ◽  
Far Field ◽  
Numerical Examples

Abstract A Landweber iteration scheme is presented for the numerical solution of an inverse obstacle problem. The method uses a recently obtained characterization of the Fréchet derivative of the far field operator and its adjoint. The performance of the method is illustrated by some numerical examples. Some theoretical aspects are pointed out to motivate the use of nonlinear Landweber iteration.

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