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Abstract
Partial differential systems which haveapplications to water waves will be formulated asexterior differential systems. A prolongation structureis determined for each of the equations. The formalismfor studying prolongations is reviewed and theprolongation equations are solved for each equation.One of thesedifferential systems includes the Camassa-Holm andDegasperis-Procesi equations as special cases.The formulation of conservation laws for eachof the systems introduced is discussedand a single example for each is given.It is shown how a Bäcklund transformationfor the last case can be obtained usingthe prolongation results.
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