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

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.

MSC:

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