Abstract
We study the generalized sine-Gordon hierarchy and its associatedη-dependent modified sine-Gordon hierarchy. Two Backlund transformations for these two families are constructed. One of them is a generalization of the Backlund transformations of Wadatiet al. and the other one is new. Gauge transformations of a relevant AKNS system are employed to reduce the integration of these equations via the Backlund transformations to quadratures. Three generations of explicit solutions of the sine-Gordon equation are presented.
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