On the three-dimensional three-wave equation with self-consistent sources

► We construct the 3D3W ESCS by allowing (a1X1+a2X2+a3X3)-dependence of the constants via SGP. ► We derive the Grammian determinant solutions of the 3D3W ESCS. ► We exam the (1,1,1)-lump solution of the 3D3W ESCS. ► We transform the 3D3W ESCS into other cases of 3D3W ESCS.