Symmetry reductions of the Lax pair for the 2 + 1-dimensional Konopelchenko–Dubrovsky equation

Based on the symbolic computational system – Maple, the similarity reduction arising from the classical Lie point symmetries of the Lax pair for the 2 + 1-dimensional Konopelchenko–Dubrovsky (KD) equation, is carried out. We obtain several interesting reductions. By analyzing not only the reduced Lax pair but also the KD equation reduced under the same symmetry group, we find that the reduced Lax pairs do not always lead to the reduced KD equation.