On the existence of vector solutions to nonlinear Schrödinger equations with weak three-wave interaction

T. Kinoshita, Y. Sato

We study a nonlinear Schrödinger system with three-wave interaction: \begin{equation*} \left\{\begin{aligned} & - Δu_1 = f_1(u_1) + αu_2u_3 \quad \text{ in } \R^N, & - Δu_2 = f_2(u…