Nonexistence of Supersonic Traveling Waves for Nonlinear Schrödinger Equations with Nonzero Conditions at Infinity

Source abstract

We prove that the nonexistence of supersonic finite-energy traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity is a general phenomenon which holds for a large class of equations. The same is true for sonic traveling waves in two dimensions. In higher dimensions we prove that sonic traveling waves, if they exist, must approach their limit at infinity in a very rigid way. In particular, we infer that there are no sonic traveling waves with finite energy and finite momentum.