Abstract
In this Letter, a three-dimensional three-wave equation with self-consistent sources (3D3W ESCS) is constructed via the source generation procedure. The corresponding Grammian determinant solutions are then derived. As a simple case, the (1,1,1)-lump solution is subsequently examined. A new feature of this 3D3W ESCS is that we allow (a1X1+a2X2+a3X3)-dependence of the arbitrary constants in the determinant solution for the three-dimensional three-wave equation while applying the source generation procedure. Finally, we show how this new system is reduced to other systems with self-consistent sources.
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