Standing waves of some coupled nonlinear Schrödinger equations

By A. Ambrosetti, Eduardo Colorado. 2007

466 citations recorded by the source corpus.

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Citations in the corpus

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.”
Ground States and Bound States of a Nonlinear Schrödinger System (2010, methodology): “Partial results on the existence of nontrivial ground states of higher dimensional systems were also given in [3, 26].”
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].”
Positive solutions for a weakly coupled nonlinear Schrödinger system (2006, result): “After this work was completed, we became aware of [4,5] in which there are some results related to ours and of [8,30] also concerning this subject.”
Uniqueness of Positive Solutions for a Nonlinear Elliptic System (2009, background): “We refer to [1,3,6,8–10,13,14] and references therein.”
An Introduction to Nonlinear Functional Analysis and Elliptic Problems (2011, background): “7 For other results dealing with nonlinearly coupled NLS equations we refer to [11].”
Multipulse Phases in k-Mixtures of Bose–Einstein Condensates (2008, methodology): “We refer the reader to the recent papers [1, 10, 6, 9, 17] mainly dealing with systems of two equations.”
Stable solitary waves with prescribed $L^2$-mass for the cubic Schr\"odinger system with trapping potentials (2014, background): “Most of them are concerned with the case of fixed chemical potentials; as a few example we quote here the papers [18, 20, 3, 7, 31, 19, 35, 6, 12, 24, 36, 11, 27, 32, 34], referring to their bibliography for an extensive list of references on this topic.”
Positive Least Energy Solutions and Phase Separation for Coupled Schrödinger Equations with Critical Exponent (2012, background): “In the subcritical case p < 2∗/2, the existence of solutions have received great interest recently, see [4, 7, 18, 24, 25, 27, 29, 34] and references therein.”
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.”
Multiple positive normalized solutions for nonlinear Schrödinger systems (2017, background): “1) where (λ1,λ2) are given has been, starting from the pioneering papers [2, 13, 27, 30, 36], the subject of a huge literature in the recent years.”
Positive least energy solutions and phase separation for coupled Schrödinger equations with critical exponent: higher dimensional case (2015, background): “In the subcritical case p < 2∗/2, the existence of solutions has received great interest recently, see [4,7,14,19,25,26,28,30,35] and references therein.”