Ground State of N Coupled Nonlinear Schrödinger Equations in Rn,n≤3

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Least Energy Solitary Waves for a System of Nonlinear Schrödinger Equations in $${\mathbb{R}^n}$$ (2007, background): “Remark 1. It was shown in [ 16 ] that A is attained if 0 16 ] that A is not attained when β 16 ] for small positive values of β. The same proof can be shown to be valid in our case, thanks to what we already proved, in particular inequalities (23)‐(28) and Lemma 3.2.”
Multi-bump solitons to linearly coupled systems of nonlinear Schrödinger equations (2007, background): “The case in which the coupling is nonlinear has been studied in [5, 18, 21, 22], see also [4, 16].”
Segregated and Synchronized Vector Solutions for Nonlinear Schrödinger Systems (2013, background): “Systems of nonlinear Schrödinger equations have been the subject of extensive mathematical studies in recent years, for example, [2–6,8–10,14,15,17,18,20,21, 24,25,29,30,34] and references therein.”
Multipulse Phases in k-Mixtures of Bose–Einstein Condensates (2008, unknown): “For the general k–systems we refer to [ 8 , 14] and the references therein.”
Bound and ground states of coupled nonlinear Schrödinger equations (2006, methodology): “Motivated by the recent paper [ 5 ], we deal here with the case in which g(u,v) = 12u 2 v2,”
A natural constraint approach to normalized solutions of nonlinear Schr\"odinger equations and systems (2016, background): “[2,10,15,25,28,29,31,38,40,41,42,51,53] and the references therein, while problem (1.”