Abstract
The three-wave resonant interaction in 1+1 dimensions is studied systematically within the prolongation scheme, which turns out to be a convenient framework for handling this process. Our analysis is carried out via a method which exploits both theSL3,c algebra associated with the three-wave equations and integrability requirements. Our procedure, which may be applied to other nonlinear evolution equations, works without fixing from the start representations of the algebra, and in the case of pseudopotentials with an arbitrary number of components. Backlund transformations which provide known and new explicit solutions are found, and inherent symmetry properties are discovered.
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