Lie symmetries, conservation laws and analytical solutions for two-component integrable equations

In this paper, two-component integrable equations, which can be used to describe many physical phenomena, are investigated. The Lie symmetry method is used to study their vector fields and optimal systems. Furthermore, the symmetry reductions and conservation laws of the equations are obtained on the basis of the optimal systems. Finally, based on the power series theory, a kind of explicit power series solutions for the equations are constructed with a detailed derivation.