Abstract
The homogeneous balance method is extended to search for Bäcklund transformation and similarity reduction of nonlinear partial differential equations. It is shown that there exist close connections among the homogeneous balance method, WTC method and CK direct reduction method. The variant Boussinesq equations are discussed as an illustrative example. Their Bäcklund transformation, linearization transformation and three types of similarity reductions are obtained. In the meantime, some new travelling wave solutions also are found.
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