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Continuity of the scattering function and Levinson‐type formula of Klein–Gordon equation
Author(s) -
Karaman Özkan,
Kosar Nida P.
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2707
Subject(s) - mathematics , klein–gordon equation , type (biology) , mathematical physics , mathematical analysis , function (biology) , physics , quantum mechanics , nonlinear system , ecology , evolutionary biology , biology
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.