Continuity of the scattering function and Levinson-type formula of Klein-Gordon equation

Continuity of the scattering function and Levinson-type formula of Klein-Gordon equation

We considered the inverse problem of scattering theory for a boundary value problem on the half line generated by Klein–Gordon differential equation with a nonlinear spectral parameter‐dependent boundary condition. We defined the scattering data, and we proved the continuity of the scattering functi...

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Veröffentlicht in:Mathematical methods in the applied sciences 2013-08, Vol.36 (12), p.1583-1590
Hauptverfasser: Karaman, Özkan, Kosar, Nida P.
Format: Artikel
Sprache:eng
Schlagworte:
Continuity
Differential equations
Gelfand-Levitan-Marchenko equation
inverse problem on half line
Klein-Gordon equation
Levinson-type formula
Mathematical analysis
Scattering
scattering data
scattering function
Scattering functions
Studies
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Zusammenfassung:We considered the inverse problem of scattering theory for a boundary value problem on the half line generated by Klein–Gordon differential equation with a nonlinear spectral parameter‐dependent boundary condition. We defined the scattering data, and we proved the continuity of the scattering function S(λ); in a special case, the relation for the difference of the logarithm of the scattering function, which is called the Levinson‐type formula, was obtained. Copyright © 2012 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.2707