Bound and ground states of coupled nonlinear Schrödinger equations

By A. Ambrosetti, Eduardo Colorado. 2006

247 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8294ff3e8643175a43c2dc7e193b28d34579337b

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Semiclassical states for weakly coupled nonlinear Schrödinger systems (2008, background): “Recently, this problem has been tackled in [2, 3, 7, 17, 18, 25] by different methods.”
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].”
Ground States and Bound States of a Nonlinear Schrödinger System (2010, methodology): “In the case of the 2-system (there is only one coupling constant β := β12 = β21), in [2, 3, 5, 6, 20, 26] more precise estimates on the size of a β0 have been given to assure for β > β0 the existence of a nontrivial ground state solution.”
Radial Solutions and Phase Separation in a System of Two Coupled Schrödinger Equations (2008, background): “If µj > 0 as considered here, we are dealing with an attractive self-interaction of the single states |j〉, j = 1, 2.”
Bound states for a coupled Schrödinger system (2007, background): “for existence of ground and bound state solutions, in particular [3, 6, 25, 29] giving an existence result for β in the large, a result in similar spirit to ours; and [23, 28, 33, 34] for multiplicity results and semiclassical states.”
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.”
Least Energy Solitary Waves for a System of Nonlinear Schrödinger Equations in $${\mathbb{R}^n}$$ (2007, methodology): “The papers [ 2 , 3] contain also results on existence of solutions of (3) in ranges of the type β< β 0, without results on the energy of these solutions.”
Uniqueness of positive solutions to some coupled nonlinear Schrödinger equations (2011, unknown): “Finally, for N = 1 and λ1 = λ2, we prove the uniqueness of positive solution when 0 ≤ β /∈ [min{µ1, µ2},max{µ1, µ2}] and thus give a complete classification of positive solutions.”
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.”
Minimal energy solutions for cooperative nonlinear Schrödinger systems (2015, methodology): “(c) In the case of a cubic nonlinearity q = 2 the existence of a vector ground state for b > μ(ω, n) was proved by Ambrosetti, Colorado when n ∈ {2, 3} and by de Figueiredo, Lopes in the one-dimensional case, cf. Theorem 2 in [1] and Theorem 1.4 in [5].”