Abstract
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.
Highlights
The Lie symmetry method was initiated by Lie [ ] in the second half of the nineteenth century
5 Construction of conservation laws using Lie-Bäcklund symmetries we briefly present the notations and theorem which are useful for constructing conservation laws with the aid of Lie-Bäcklund symmetries
Based on the optimal system, we have considered the symmetry reductions and group invariant solutions of the Drinfeld-Sokolov-Wilson system (DSWS)
Summary
The Lie symmetry method was initiated by Lie [ ] in the second half of the nineteenth century It has become one of the most powerful methods to study nonlinear partial differential equations (NLPDEs). Application of the Lie symmetry method for constructing the explicit solutions of the NLPDEs can always be regarded as one of the most important fields of mathematical physics. Matjila et al derived the exact solutions of system ( ) by using the (G /G)-expansion function method They constructed conservation laws using Noether’s approach [ ]. In Section , we derive the Lie point symmetries of the DSWS using Lie group analysis and find the transformed solutions. In Section , the method of constructing conservation laws of NLPDEs with the aid of the new conservation theorem associated with Lie-Bäcklund symmetries is presented.
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