jats:titleAbstract</jats:title>jats:pStarting from the 3-wave interaction equations in 2+1 dimensions (i.e., two space dimensions and one time dimension), we complexify the independent variables, thus doubling the number of real variables, and hence we work in 4+2 dimensions: jats:inline-formulajats:alternativesjats:tex-math$$x_1$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msub mml:mix</mml:mi> mml:mn1</mml:mn> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>, jats:inline-formulajats:alternativesjats:tex-math$$x_2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msub mml:mix</mml:mi> mml:mn2</mml:mn> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>, jats:inline-formulajats:alternativesjats:tex-math$$y_1$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msub mml:miy</mml:mi> mml:mn1</mml:mn> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>, jats:inline-formulajats:alternativesjats:tex-math$$y_2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msub mml:miy</mml:mi> mml:mn2</mml:mn> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> and jats:inline-formulajats:alternativesjats:tex-math$$t_1$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msub mml:mit</mml:mi> mml:mn1</mml:mn> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>, jats:inline-formulajats:alternativesjats:tex-math$$t_2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msub mml:mit</mml:mi> mml:mn2</mml:mn> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>. In this paper we solve the initial value problem of the 3-wave interaction equations in 4+2 dimensions.</jats:p>