Abstract
The (constrained) canonical reduction of four dimensional self-dual Yang–Millstheory to 2, (2+1) dimensional sine-Gordon theory and 2 dimensional Liouvilles theory areconsidered. The Bäcklund transformations (BTs) areimplemented to obtain new classes of exact solutions for the reduced 2 dimensional sine-Gordonand Liouville models. Another transformation is developed and used to obtain exact solution forthe 2+1 and the original 3+1 sine-Gordon models.
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