Abstract
Abstract As an example of how to deal with nonintegrable systems, the nonlinear partial differential equation which describes the evolution of long surface waves in a convecting fluid is fully analyzed, including symmetries (nonclassical and contact transformatons), similarity reductions and the application of the ARS algorithm to the reductions. As a result of the calculations, the Galilean invariance of the equation is shown and all the possible solutions arising from the related ODE through these methods are obtained and classified in terms of the physical parameters.
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