Solving the Initial Value Problem for the 3-Wave Interaction Equations in Multidimensions

Abstract Starting from the 3-wave interaction equations in 2+1 dimensions (i.e., two space and one time dimension), we complexify independent variables, thus doubling number of real hence work 4+2 dimensions: $$x_1$$ x 1 , $$x_2$$ 2 $$y_1$$ y $$y_2$$ $$t_1$$ t $$t_2$$ . In this paper solve initial value problem dimensions.