Abstract
The symmetries of the (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations, which describe the atmospheric gravity waves (GWs), are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. Calculation shows the INHB equations are invariant under some Galilean transformations, scaling transformations, and space-time translations. The symmetry reduction equations and similar solutions of the INHB equations are proposed.
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