Principles of Limiting Absorption and Limiting Amplitude in Scattering Theory. II. The Wave Equation in an Inhomogeneous Medium

1961 ◽  
Vol 2 (6) ◽  
pp. 800-802 ◽  
Author(s):  
Farouk M. Odeh
Keyword(s):  
Wave Equation ◽  
Inhomogeneous Medium ◽  
Scattering Theory

Parabolic Representations of Scattering Green’s Functions

1999 ◽  
Author(s):  
Paul E. Barbone
Keyword(s):  
Asymptotic Expansion ◽  
Wave Equation ◽  
Green’S Function ◽  
Inhomogeneous Medium ◽  
Green's Function ◽  
Free Space ◽  
Green's Functions ◽  
Green’S Functions

Abstract We derive a one-way wave equation representation of the “free space” Green’s function for an inhomogeneous medium. Our representation results from an asymptotic expansion in inverse powers of the wavenumber. Our representation takes account of losses due to scattering in all directions, even though only one-way operators are used.

scholarly journals Scattering theory for the wave equation on a hyperbolic manifold

1987 ◽  
Vol 74 (2) ◽  
pp. 346-398 ◽  
Author(s):  
Ralph Phillips ◽  
Bettina Wiskott ◽  
Alex Woo
Keyword(s):  
Wave Equation ◽  
Scattering Theory ◽  
Hyperbolic Manifold

scholarly journals Scattering theory for the radialH˙12-critical wave equation with a cubic convolution

2015 ◽  
Vol 259 (12) ◽  
pp. 7199-7237 ◽  
Author(s):  
Changxing Miao ◽  
Junyong Zhang ◽  
Jiqiang Zheng
Keyword(s):  
Wave Equation ◽  
Scattering Theory

Scattering on Riemannian Symmetric Spaces and Huygens Principle

2018 ◽  
Vol 30 (08) ◽  
pp. 1840015
Author(s):  
Michael Semenov-Tian-Shansky
Keyword(s):  
Wave Equation ◽  
Scattering Theory ◽  
Symmetric Spaces ◽  
Evolution System ◽  
Semisimple Lie Groups ◽  
Curved Space ◽  
Zero Curvature ◽  
Famous Paper ◽  
Huygens Principle ◽  
Riemannian Symmetric Spaces

The famous paper by L. D. Faddeev and B. S. Pavlov (1972) on automorphic wave equation explored a highly romantic link between Scattering Theory (in the sense of Lax and Phillips) and Riemann hypothesis. An attempt to generalize this approach to general semisimple Lie groups leads to an interesting evolution system with multidimensional time explored by the author in 1976. In the present paper, we compare this system with a simpler one defined for zero curvature symmetric spaces and show that the Huygens principle for this system in the curved space holds if and only if it holds in the zero curvature limit.

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