Symmetry analysis and reductions of the two-dimensional generalized Benney system via geometric approach

In this work, the symmetry group and similarity reductions of the two-dimensional generalized Benney system are investigated by means of the geometric approach of an invariance group, which is equivalent to the classical Lie symmetry method. Firstly, the vector field associated with the Lie group of transformation is obtained. Then the point transformations are proposed, which keep the solutions of the generalized Benney system invariant. Finally, the symmetry reductions and explicitly exact solutions of the generalized Benney system are derived by solving the corresponding symmetry equations.