Abstract
Recently Ablowitz and Haberman have shown that, in three spatial dimensions, the nonlinear 3-wave evolution equation results from the compatibility condition between two well-defined first-order linear differential 3×3 systems having common solutions. We construct inversionlike integral equations (I.E.) associated with both these two linear differential systems so that the solutions of the I.E. embody their compatibility conditions. The scalar kernels of these I.E. depend upon three independent variables in such a way that there exist degenerate kernels confined in the three-dimensional coordinate space. Consequently we exhibit, for the nonlinear 3-wave evolution equations, an infinite number of solutions which, at fixed time, are confined in the three-dimensional coordinate space.
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