Asymptotics of the scattering operator for the wave equation in a singularly perturbed domain

2021 ◽  
Vol 212 (10) ◽  
Author(s):  
Dmitrii Vladimirovich Korikov
Keyword(s):  
Wave Equation ◽  
Singularly Perturbed ◽  
Scattering Operator ◽  
Singularly Perturbed Domain

scholarly journals GEOMETRIC-OPTICS FOR NONLINEAR CONCENTRATING WAVES IN FOCUSING AND NON-FOCUSING TWO GEOMETRIES

2004 ◽  
Vol 06 (01) ◽  
pp. 1-23 ◽  
Author(s):  
SLIM IBRAHIM
Keyword(s):  
Wave Equation ◽  
Geometrical Optics ◽  
Variable Coefficients ◽  
Geometric Optics ◽  
Scattering Operator ◽  
Wave Operators

With the methods used in [1] and [4], we prove that in the absence of focus, nonlinear geometrical optics of the critical wave equation with variable coefficients, is reduced to linear geometrical optics combined with wave operators for the critical wave equation with coefficients fixed on concentrating points. On the odd-dimensional spheres, we prove that passing through a focus is generated by a modified scattering operator.

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