Solitary waves with non-vanishing angular momentum. (English) Zbl 1030.35051

Benci, Vieri; Visciglia, Nicola

Adv. Nonlinear Stud. 3, No. 1, 151-160 (2003).

Consider the following nonlinear Schrödinger equation: \[ i\frac{\partial\varphi}{\partial t}=-\frac{1}{2}\Delta \varphi-|\varphi|^{p-2}\varphi,\tag{1} \] where \(\varphi:\mathbb{R}^3\times \mathbb{R}\to C\) and \(2<p<6.\) Then it has been known that equation (1) admits solitary waves having vanishing momentum and angular momentum. In this paper, the authors are interested in the existence of standing waves with nonvanishing angular momentum. To prove the existence results, the authors employ the concentration compactness due to P. L. Lions.

Reviewer: Yuxia Guo (Beijing)

MSC:

35J60	Nonlinear elliptic equations
46B50	Compactness in Banach (or normed) spaces

Keywords:

concentration compactness; constrained minimization; extendibility of solutions; solitary waves