Classical Symmetry Reductions of the Schwarz–Korteweg–de Vries Equation in $2+1$ Dimensions

Classical reductions of a $(2+1)$-dimensional integrable Schwarz–Korteweg–de Vries equation are classified. These reductions to systems of partial differential equations in $1+1$ dimensions admit symmetries that lead to further reductions, i.e., to systems of ordinary differential equations. All these systems have been reduced to second-order ordinary differential equations. We present some particular solutions involving two arbitrary functions.