Solutions with expanding compact support of saturated Schr{ö}dinger equations: self-similar solutions

Pascal Bégout, Jesus Ildefonso Diaz

We prove the existence of solutions \(u(t,x)\) of the Schr{ö}dinger equation with a saturation nonlinear term \((u/|u|)\) having compact support, for each \(t>0,\) that expands wit…