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X iv :2 11 1. 09 48 2v 1 [ nl in .P S] 1 8 N ov 2 02 1 Higher-dimensional soliton generation, stability and excitations of the PT -symmetric nonlinear Schrödinger equations Yong Chen1, Zhenya Yan2,3,∗ , Boris A. Malomed4,5 1 School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China 2Key Lab of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 3School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China 4Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv 69978, Israel 5Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile