# zbMATH — the first resource for mathematics

More self-similar solutions of the nonlinear Schrödinger equation. (English) Zbl 0990.35121
Summary: We prove the existence of self-similar solutions of the Schrödinger equation in $${\mathbb R}^N$$ with power nonlinearity $$\gamma|u|^\alpha u$$. Existence is obtained for a range of $$\alpha$$ given by $$a< \alpha< 4/(n-4)$$, $$n\geq 3$$ where $$(n-2)\alpha^2+ (n-4)\alpha-4=0$$, which differs from, but overlaps with, the range of powers considered in [Math. Z. 228, 83-120 (1998; Zbl 0916.35109)]. We also obtain regularity results for the self-similar solutions constructed in [loc. cit].

##### MSC:
 35Q55 NLS equations (nonlinear Schrödinger equations) 35D05 Existence of generalized solutions of PDE (MSC2000) 35D10 Regularity of generalized solutions of PDE (MSC2000) 35B60 Continuation and prolongation of solutions to PDEs
Full Text: