The variable coefficient Boiti–Leon–Pempinelli and similar systems: The Lie symmetry approach

Abstract

We consider the variable coefficient Boiti–Leon–Pempinelli and two similar systems. We present the enhanced Lie group classification. This task is achieved with the aid of the equivalence transformations. We construct a number of similarity reductions which are used to derive exact solutions for the three ‐dimensional systems. The reductions are obtained using both one‐ and two‐dimensional subalgebras. In a specific case, each system admits a hidden symmetry.