Abstract
The symmetry algebra of an integrable dispersive long-wave equation in two space dimensions is shown to be infinite-dimensional and to have a Kac-Moody-Virasoro structure. The corresponding symmetry group is used to generate a large number of new solutions, in particular solitons, kinks and periodic waves. These waves have wave crests of quite general shapes. The results are compared to those for a nonintegrable two-space-dimensional dispersive long-wave equation, for which the symmetry group is finite-dimensional and wave crests are always straight lines.
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