Inverse scattering problem for the non-stationary matrix Dirac equation on the half-plane with the singular transmission matrix in the boundary condition

2015 ◽  
Author(s):  
Ibrahim Tekin ◽  
Mansur I. Ismailov
Keyword(s):  
Boundary Condition ◽  
Dirac Equation ◽  
Inverse Scattering ◽  
Half Plane ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Transmission Matrix

Inverse scattering problem for the nonstationary Dirac equation on the half-plane

2016 ◽  
Vol 24 (3) ◽  
Author(s):  
Mansur I. Ismailov
Keyword(s):  
Boundary Condition ◽  
Dirac Equation ◽  
Inverse Scattering ◽  
Half Plane ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Dirac System ◽  
Scattering Operator ◽  
Uniqueness Criterion

AbstractIn this paper, the inverse scattering problem for the nonstationary Dirac system on the half-plane is considered. The uniqueness criterion for the inverse scattering problem in terms of boundary condition is described and the restoration of the potential from the scattering operator is proved.

Far field patterns and inverse scattering problems for imperfectly conducting obstacles

1989 ◽  
Vol 106 (3) ◽  
pp. 553-569 ◽  
Author(s):  
T. S. Angell ◽  
David Colton ◽  
Rainer Kress
Keyword(s):  
Boundary Condition ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Plane Waves ◽  
Inverse Scattering Problem ◽  
Impedance Boundary Condition ◽  
Far Field ◽  
Scattering Problems ◽  
Impedance Boundary ◽  
Field Patterns

AbstractWe first examine the class of far field patterns for the scalar Helmholtz equation in ℝ2 corresponding to incident time harmonic plane waves subject to an impedance boundary condition where the impedance is piecewise constant with respect to the incident direction and continuous with respect to x ε ∂ D where ∂ D is the scattering obstacle. We then examine the class of far field patterns for Maxwell's equations in subject to an impedance boundary condition with constant impedance. The results obtained are used to derive optimization algorithms for solving the inverse scattering problem.

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