Continuity of the scattering function and Levinson‐type formula of Klein–Gordon equation | Zendy

Karaman Özkan | Zendy; Kosar Nida P. | Zendy

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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.

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