Scattering problem for the Schr�dinger equation in the case of a potential linear in time and coordinate. I. Asymptotics in the shadow zone

1986 ◽  
Vol 32 (2) ◽  
pp. 103-112 ◽  
Author(s):  
V. M. Babich ◽  
V. P. Smyshlyaev
Keyword(s):  
Scattering Problem ◽  
Shadow Zone ◽  
Dinger Equation

scholarly journals Scattering Problem for the Supercritical Nonlinear Schrödinger Equation in 1d

2015 ◽  
Vol 58 (3) ◽  
pp. 451-470
Author(s):  
Nakao Hayashi ◽  
Pavel I. Naumkin
Keyword(s):  
Scattering Problem ◽  
Dinger Equation

scholarly journals The relation of Zakharov-Shabat scattering problem to Schrödinger equation with complex potential and approximations for soliton parameters

2019 ◽  
Vol 65 (6 Nov-Dec) ◽  
pp. 634
Author(s):  
N. Korneev ◽  
J. A. Catana ◽  
V. A. Vyslooukh
Keyword(s):  
Schrödinger Equation ◽  
High Power ◽  
Complex Potential ◽  
Schrodinger Equation ◽  
Scattering Problem ◽  
Dinger Equation ◽  
Kerr Media ◽  
Different Types

The relation of Zakharov-Shabat scattering problem to Schr\"{o}dinger equation with complex potential is used to analytically approximate parameters of high power solitons produced in positive Kerr media with chirped parabolic pulses. The soliton parameters are estimated for different types of chirp and intensity distortions. The comparison with numerics is discussed.

Application of Kirchhoff’s Integral Equation Formulation to an Elastic Wave Scattering Problem

1967 ◽  
Vol 34 (4) ◽  
pp. 921-930 ◽  
Author(s):  
William L. Ko ◽  
Thorbjorn Karlsson
Keyword(s):  
Wave Front ◽  
Integral Equations ◽  
Scattering Problem ◽  
Linear Matrix ◽  
Infinite Length ◽  
Shadow Zone ◽  
Surface Integral ◽  
Front Solution ◽  
Frequency Wave ◽  
Integral Equation Formulation

Interaction of a plane compressional step wave with a circular cylindrical obstacle embedded in an elastic medium is studied. The obstacle is rigid, stationary, and of infinite length. The incident wave travels in a direction perpendicular to the axis of the cylinder. Using Kirchhoff’s theorem, surface integral equations are formulated for the displacement potential derivatives in the scattered field and on the cylinder boundary. The wave-front solution obtained for the illuminated zone on the cylinder is identical to that obtained by high-frequency wave-front analysis. Boundary stresses in the shadow zone as well as the initial behavior of the wave-front stresses at the boundary between the illuminated and shadow zones are obtained. The integral equations for both illuminated and shadow-zone boundary stresses are reduced to successive linear matrix equations for numerical analysis. The numerical methods developed in this paper can be applied to interaction problems for obstacles of arbitrary geometrical configuration. They are also readily extended to the case where the medium exhibits bilinear or multilinear stress-strain behavior.

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