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The symmetry analysis method is used to study the Drinfeld-Sokolov-Wilson system. The Lie point symmetries of this system are obtained. An optimal system of one-dimensional subalgebras is derived by using Ibragimov’s method. Based on the optimal system, similarity reductions and explicit solutions of the system are presented. The Lie-Bäcklund symmetry generators are also investigated. Furthermore, the method of constructing conservation laws of nonlinear partial differential equations with the aid of a new conservation theorem associated with Lie-Bäcklund symmetries is presented. Conservation laws of the Drinfeld-Sokolov-Wilson system are constructed by using this method.

Lie symmetry analysis, Lie-Bäcklund symmetries, explicit solutions, and conservation laws of Drinfeld-Sokolov-Wilson system