Least Energy Solitary Waves for a System of Nonlinear Schrödinger Equations in $${\mathbb{R}^n}$$

375 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Uniqueness of Positive Solutions for a Nonlinear Elliptic System (2009, background): “(iii) Uniqueness of nontrivial positive solution of (1)–(4) does not hold for all β> 0. Indeed, the following example is given in [ 13 ]; let V1(x) ≡ V2(x) ≡ 1, µ1 = µ2 = β =1a ndω1 be a positive solution of −∆u1 + u1 = u 3 in R N .”
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].”
Radial Solutions and Phase Separation in a System of Two Coupled Schrödinger Equations (2008, background): “... belonging to different subintervals of (0, ∞). It is important to note that when � is a ball or � = R N and β> 0, then all solutions of (1.2) are radially symmetric (up to translation if � = R N ), and both components are decreasing in the radial variable,see[42].Incontrast,differentclassesofnon”
Positive solutions for a weakly coupled nonlinear Schrödinger system (2006, result): “Remark 6.6. After this work was completed, we became aware of [4] and [5] in which there are some results related to ours and of [8], [ 35 ] also concerning this subject.”
Ground States and Bound States of a Nonlinear Schrödinger System (2010, background): “Schrödinger systems, nonlinear couplings, co-existing ground states, multiple bound states”