The nonlinear Schrödinger equation with combined power-type nonlinearities

Terence Tao, Monica Visan, Xiaoyi Zhang

We undertake a comprehensive study of the nonlinear Schrödinger equation $$i{u}_t+\Delta u={\lambda }_1|u{|}^{p_1}u+{\lambda }_2|u{|}^{p_2}u,$$ where $u(t,x)$ is a complex-valued function in spacetime…