On the existence of self-similar solutions of the nonlinear Schrödinger equation with power nonlinearity between 1 and 2

Abstract

We improve on a previous result by Ribaud and Youssfi on existence of self-similar solutions for the nonlinear Schrödinger equation, extending the range of available nonlinearities $\alpha +1 $ to $\alpha$ smaller than 1. We exploit the different behavior of the linear and nonlinear terms.