Spikes in Two-component Systems of Nonlinear Schrodinger Equations with Trapping Potentials

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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.”
A priori bounds versus multiple existence of positive solutions for a nonlinear Schrödinger system (2010, background): “In [18], the asymptotic behavior is studied in R under the influence of nonconstant trapping potentials.”
Ground States and Bound States of a Nonlinear Schrödinger System (2010, background): “For examples, following the work [16] by Lin and Wei about the existence of ground state solutions with small couplings for a general N -system, a number of papers have been devoted to the existence theory of solutions for the 2-system in various different parameter regimes of nonlinear couplings; s”
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.”
Bound states for a coupled Schrödinger system (2007, result): “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.”