Open AccessIntegrability of Klein–Gordon Equations
Author(s) -
Peter A. Clarkson,
John Mcleod,
Peter J. Olver,
A. Ramani
Publication year - 1986
Publication title -
siam journal on mathematical analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.882
H-Index - 92
eISSN - 1095-7154
pISSN - 0036-1410
DOI - 10.1137/0517058
Subject(s) - integrable system , mathematics , mathematical physics , nonlinear system , sine , klein–gordon equation , exponential function , mathematical analysis , sine gordon equation , soliton , physics , quantum mechanics , geometry
Using the Painleve test, it is shown that the only integrable nonlinear Klein–Gordon equations $u_{xt} = f(u)$ with f a linear combination of exponentials are the Liouville, sine-Gordon (or sink-Gordon) and Mikhailov equations. In particular, the double sine-Gordon equation is not integrable.
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