On integrable properties for two variable-coefficient evolution equations

With the help of the extended binary Bell polynomials, the new bilinear representations, Bäcklund transformations, Lax pair and infinite conservation laws for two types of variable-coefficient nonlinear integrable equations are obtained, respectively, which are more straightforward than previous corresponding results obtained. Finally, we obtain new multi-soliton wave solutions of a reduced soliton equations with variable coefficients.