Abstract
AbstractIn this paper, we show the scattering and blow up result of the solution for some coupled nonlinear Schrödinger system with static energy less than that of the ground state in , where . 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 nonlinear Schrödinger system. Copyright © 2013 John Wiley & Sons, Ltd.
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