Abstract
New exact Grammian determinant solutions to two (3+1)-dimensional nonlinear evolution equations are derived. Extended set of sufficient conditions consisting of linear partial differential equations with variable-coefficients is presented. Moreover, a systematic analysis of linear partial differential equations is used for solving the representative linear systems. The bilinear Bäcklund transformations are also constructed for the equations. Also, as an application of the bilinear Bäcklund transforms, a new class of wave and rational solutions to the equations are explicitly computed.