Final state problem for a quadratic nonlinear Schrödinger system in two space dimensions with mass resonance

We consider the asymptotic behavior of a solution to a quadratic nonlinear Schrödinger system in two space dimensions. We construct a particular solution which describes the charge dissipation phenomenon in spite of the mass preserving structure of the system. This is a consequence of a new explicit solution to a system of ordinary differential equation which approximates asymptotic behavior of a solution to the system.