Integral equations on a half-line with kernel depending upon the difference of the arguments

1962 ◽  
pp. 163-288 ◽  
Author(s):  
M. G. Kreĭn
Keyword(s):  
Integral Equations ◽  
Half Line ◽  
The Difference

Diffraction by a wave-guide of finite length

1952 ◽  
Vol 48 (1) ◽  
pp. 118-134 ◽  
Author(s):  
D. S. Jones
Keyword(s):  
Electromagnetic Wave ◽  
Approximate Solution ◽  
Laplace Transform ◽  
Integral Equations ◽  
Finite Length ◽  
Wave Guide ◽  
The Laplace Transform ◽  
The Difference

AbstractWhen the electric intensities on two parallel planes, of which the two perfectly conducting sides of a wave-guide of finite length and infinite width are portions, are taken as unknowns, the problem of the diffraction of a plane harmonic electromagnetic wave polarized parallel to the edges of the guide leads to two integral equations. By means of the Laplace transform these equations are converted into others suitable for solution by successive substitutions. The series thus obtained is too complex for practical purposes, and so an approximate solution is found for the case when the length of the guide is large compared with the wavelength. Finally, there is a brief discussion of the difference between the distant fields when l is large and when l is infinite.

scholarly journals FIRST ORDER QUANTUM CORRECTIONS TO THE CLASSICAL REFLECTION FACTOR OF THE SINH–GORDON MODEL

2000 ◽  
Vol 15 (28) ◽  
pp. 4417-4432 ◽  
Author(s):  
A. CHENAGHLOU ◽  
E. CORRIGAN
Keyword(s):  
Boundary Conditions ◽  
Quantum Corrections ◽  
Half Line ◽  
Reflection Factor ◽  
Loop Order ◽  
Perturbative Calculation ◽  
First Order ◽  
The Difference ◽  
Two Parameters

The sinh–Gordon model is restricted to a half-line by boundary conditions maintaining integrability. A perturbative calculation of the reflection factor is given to one loop order in the bulk coupling and to first order in the difference of the two parameters introduced at the boundary, providing a further verification of Ghoshal's formula. The calculation is consistent with a conjecture for the general dependence of the reflection factor on the boundary parameters and the bulk coupling.

Sign in / Sign up

Export Citation Format

Share Document