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Two new applications of the homogeneous balance method. (English) Zbl 0947.35012
Summary: 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.
MSC:
35A30Geometric theory for PDE, characteristics, transformations
58J72Correspondences and other transformation methods (PDE on manifolds)
35G20General theory of nonlinear higher-order PDE