Double reductions/analysis of the Drinfeld–Sokolov–Wilson equation

In this paper, we show that the recently developed formulation of the association between symmetries and conservation laws lead to double reductions of the third-order Drinfeld–Sokolov–Wilson system of partial differential equations (PDEs). For illustrative purposes only, we carry out the procedure for a version of the well-known third-order scalar Korteweg–de Vries (KdV) equation via a scaling symmetry of the equation.