2013
DOI: 10.1002/mma.3015
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Dynamics of some coupled nonlinear Schrödinger systems in

Abstract: In this paper, we show the scattering and blow up result of the solution for some coupled nonlinear Schrödinger system We first use the Nehari manifold approach and the Schwarz symmetrization technique to construct the ground state and obtain the threshold energy of scattering solution, then use Payne-Sattinger's potential well argument and Kenig-Merle's compactness-rigidity argument to show the aforementioned dichotomy result. As we know, it is the first attempt to show the scattering result for the coupled n… Show more

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Cited by 11 publications
(18 citation statements)
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“…Recalling the scattering and blow‐up result of , which established by Xu (Theorem 1.2 of Xu), which is…”
Section: Introductionmentioning
confidence: 99%
See 4 more Smart Citations
“…Recalling the scattering and blow‐up result of , which established by Xu (Theorem 1.2 of Xu), which is…”
Section: Introductionmentioning
confidence: 99%
“…System is an important model in physics, which is a good approximation describing the propagation of self‐trapped mutually incoherent wave packets in nonlinear optics. For more phsical background of , one can see Xu and references therein. This paper just focuses on the two coupled nonlinear Schrödinger system .…”
Section: Introductionmentioning
confidence: 99%
See 3 more Smart Citations