For a certain range of the value in the nonlinear term , in this paper we mainly study the global existence and uniqueness of global self-similar solutions to the Cauchy problem for some nonlinear Schrödinger equations using the method of harmonic analysis.
"Global Self-similar Solutions of a Class of Nonlinear Schrödinger Equations." Abstr. Appl. Anal. 2008 1 - 9, 2008. https://doi.org/10.1155/2008/836124