(Received October 8, 1986)
We have considered the complete integrability of two nonlinear equations which are some kind of extensions of usual sine-Gordon and sinh-Gordon equations. The first one is of non-autonomous version of sinh-Gordon system and the second is closely related to the usual sine-Gordon theory. The first problem indicates how (x,t) dependent nonlinear equations can be treated in the prolongation theory and how a Bäcklund map can be constructed. The second one is a variation of the usual sine-Gordon equation and suggests that there may be other equations (similar to sine-Gordon) which are completely integrable. In both the cases we have been able to construct the Lax pair. We then construct an auto-Bäcklund map by following the idea of Konno and Wadati, for the generation of multisolution states.
URL : http://ptp.ipap.jp/link?PTP/77/232/
DOI : 10.1143/PTP.77.232