Integrability of Klein–Gordon Equations
Authors:
- Peter A. ClarksonPCPeter A. Clarkson
- J. Bryce McLeodJMJ. Bryce McLeod
- Peter J. OlverPOPeter J. Olver
- Alfred RamaniARAlfred Ramani
- 1 July 1986
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 17 (4) , 798-802
Abstract
Using the Painlevé 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.
Keywords
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